total num of chars: 20 total num of families: 10 chars where some sequence of nonzero coeffs is not unimodal in abs value: 3.1 = 62 in family 3.1 = 62 chars where some polynomial has both positive and negative coeffs: 3.1 = 62 in family 3.1 = 62 chars where some polynomial has strictly negative coeffs: 1.111 = 221111 in family 1.111 = 221111 3.1 = 62 in family 3.1 = 62 11.11 = 2222 in family 11.11 = 2222 2.11 = 4211 in family 2.11 = 4211 | 7 elements where some sequence of nonzero coeffs is not unimodal in abs value. 3.1 = 62 in family 3.1 = 62 #260 [ 3, 2, 1, 2, 3, 4, 3, 2, 1, 2 ] #264 [ 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #266 [ 2, 1, 2, 3, 2, 1, 2, 4, 3, 2 ] #274 [ 2, 3, 2, 1, 2, 4, 3, 2, 1, 2 ] #299 [ 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #304 [ 2, 1, 2, 3, 2, 4, 3, 2, 1, 2, 3 ] #306 [ 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2 ] | 3 elements where some polynomial has both positive and negative coeffs. 3.1 = 62 in family 3.1 = 62 #260 [ 3, 2, 1, 2, 3, 4, 3, 2, 1, 2 ] #264 [ 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #299 [ 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] | 235 elements where some polynomial has strictly negative coeffs. 3.1 = 62 in family 3.1 = 62 #34 [ 4, 3, 2, 1 ] #36 [ 3, 2, 1, 4 ] #40 [ 2, 1, 4, 3 ] #44 [ 2, 1, 3, 4 ] #48 [ 1, 4, 3, 2 ] #50 [ 1, 3, 2, 4 ] #52 [ 1, 2, 4, 3 ] #54 [ 1, 2, 3, 4 ] #56 [ 4, 3, 2, 1, 2 ] #57 [ 3, 2, 1, 2, 4 ] #58 [ 2, 1, 2, 4, 3 ] #59 [ 2, 1, 2, 3, 4 ] #60 [ 3, 4, 3, 2, 1 ] #63 [ 3, 2, 1, 4, 3 ] #64 [ 2, 4, 3, 2, 1 ] #67 [ 2, 1, 4, 3, 2 ] #70 [ 2, 3, 2, 1, 4 ] #71 [ 2, 1, 3, 4, 3 ] #72 [ 2, 1, 3, 2, 4 ] #76 [ 1, 4, 3, 2, 1 ] #77 [ 1, 3, 4, 3, 2 ] #78 [ 1, 3, 2, 1, 4 ] #80 [ 1, 2, 1, 4, 3 ] #81 [ 1, 2, 4, 3, 2 ] #83 [ 1, 3, 2, 4, 3 ] #84 [ 1, 2, 1, 3, 4 ] #85 [ 1, 2, 3, 4, 3 ] #86 [ 1, 2, 3, 2, 4 ] #87 [ 4, 3, 2, 1, 2, 3 ] #88 [ 3, 2, 1, 2, 3, 4 ] #89 [ 3, 4, 3, 2, 1, 2 ] #90 [ 3, 2, 1, 2, 4, 3 ] #91 [ 2, 1, 2, 3, 4, 3 ] #94 [ 2, 1, 2, 4, 3, 2 ] #95 [ 2, 1, 2, 3, 2, 4 ] #96 [ 3, 2, 4, 3, 2, 1 ] #97 [ 3, 2, 1, 4, 3, 2 ] #98 [ 2, 4, 3, 2, 1, 2 ] #100 [ 2, 1, 4, 3, 2, 1 ] #102 [ 2, 3, 2, 1, 4, 3 ] #103 [ 2, 3, 4, 3, 2, 1 ] #104 [ 2, 3, 2, 1, 2, 4 ] #105 [ 2, 1, 3, 2, 1, 4 ] #106 [ 2, 1, 3, 4, 3, 2 ] #107 [ 2, 1, 3, 2, 4, 3 ] #113 [ 1, 3, 4, 3, 2, 1 ] #116 [ 1, 2, 1, 4, 3, 2 ] #118 [ 1, 2, 4, 3, 2, 1 ] #119 [ 1, 3, 2, 4, 3, 2 ] #120 [ 1, 3, 2, 1, 4, 3 ] #121 [ 1, 2, 1, 3, 2, 4 ] #122 [ 1, 2, 1, 3, 4, 3 ] #123 [ 1, 2, 3, 4, 3, 2 ] #124 [ 1, 2, 3, 2, 1, 4 ] #125 [ 1, 2, 3, 2, 4, 3 ] #126 [ 4, 3, 2, 1, 2, 3, 4 ] #127 [ 3, 2, 1, 2, 3, 4, 3 ] #128 [ 3, 4, 3, 2, 1, 2, 3 ] #130 [ 3, 2, 1, 2, 4, 3, 2 ] #131 [ 2, 4, 3, 2, 1, 2, 3 ] #132 [ 2, 3, 2, 1, 2, 3, 4 ] #134 [ 2, 1, 2, 4, 3, 2, 1 ] #135 [ 2, 1, 2, 3, 2, 1, 4 ] #136 [ 2, 1, 2, 3, 4, 3, 2 ] #137 [ 3, 2, 4, 3, 2, 1, 2 ] #138 [ 3, 2, 1, 4, 3, 2, 1 ] #140 [ 2, 1, 2, 3, 2, 4, 3 ] #141 [ 2, 3, 2, 4, 3, 2, 1 ] #142 [ 2, 3, 2, 1, 4, 3, 2 ] #143 [ 2, 3, 4, 3, 2, 1, 2 ] #144 [ 2, 3, 2, 1, 2, 4, 3 ] #146 [ 2, 1, 3, 4, 3, 2, 1 ] #147 [ 2, 1, 3, 2, 1, 4, 3 ] #148 [ 2, 1, 3, 2, 4, 3, 2 ] #160 [ 1, 2, 4, 3, 2, 1, 2 ] #161 [ 1, 3, 2, 4, 3, 2, 1 ] #162 [ 1, 3, 2, 1, 4, 3, 2 ] #163 [ 1, 2, 1, 3, 2, 4, 3 ] #165 [ 1, 2, 1, 3, 4, 3, 2 ] #166 [ 1, 2, 3, 2, 1, 2, 4 ] #167 [ 1, 2, 3, 4, 3, 2, 1 ] #168 [ 1, 2, 3, 2, 4, 3, 2 ] #169 [ 1, 2, 3, 2, 1, 4, 3 ] #170 [ 3, 4, 3, 2, 1, 2, 3, 4 ] #174 [ 3, 2, 1, 2, 3, 4, 3, 2 ] #175 [ 3, 2, 4, 3, 2, 1, 2, 3 ] #176 [ 3, 2, 1, 2, 4, 3, 2, 1 ] #177 [ 2, 4, 3, 2, 1, 2, 3, 4 ] #178 [ 2, 1, 4, 3, 2, 1, 2, 3 ] #179 [ 2, 1, 3, 2, 1, 2, 3, 4 ] #180 [ 2, 1, 2, 3, 4, 3, 2, 1 ] #181 [ 3, 2, 1, 4, 3, 2, 1, 2 ] #182 [ 2, 3, 2, 1, 2, 3, 4, 3 ] #183 [ 2, 1, 2, 3, 2, 1, 4, 3 ] #184 [ 2, 1, 2, 3, 2, 4, 3, 2 ] #185 [ 2, 3, 2, 4, 3, 2, 1, 2 ] #186 [ 2, 3, 2, 1, 4, 3, 2, 1 ] #187 [ 2, 3, 2, 1, 2, 4, 3, 2 ] #188 [ 2, 3, 4, 3, 2, 1, 2, 3 ] #191 [ 2, 1, 3, 2, 1, 4, 3, 2 ] #192 [ 2, 1, 3, 2, 4, 3, 2, 1 ] #198 [ 1, 2, 4, 3, 2, 1, 2, 3 ] #199 [ 1, 2, 3, 2, 1, 2, 3, 4 ] #205 [ 1, 3, 2, 4, 3, 2, 1, 2 ] #206 [ 1, 3, 2, 1, 4, 3, 2, 1 ] #207 [ 1, 2, 1, 2, 3, 2, 4, 3 ] #208 [ 1, 2, 1, 3, 2, 1, 4, 3 ] #209 [ 1, 2, 1, 3, 2, 4, 3, 2 ] #212 [ 1, 2, 3, 4, 3, 2, 1, 2 ] #213 [ 1, 2, 3, 2, 1, 2, 4, 3 ] #214 [ 1, 2, 3, 2, 4, 3, 2, 1 ] #215 [ 1, 2, 3, 2, 1, 4, 3, 2 ] #221 [ 3, 2, 4, 3, 2, 1, 2, 3, 4 ] #222 [ 3, 2, 1, 2, 3, 4, 3, 2, 1 ] #223 [ 3, 2, 1, 4, 3, 2, 1, 2, 3 ] #224 [ 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #225 [ 2, 3, 2, 1, 2, 3, 4, 3, 2 ] #226 [ 2, 3, 4, 3, 2, 1, 2, 3, 4 ] #227 [ 2, 1, 3, 2, 1, 2, 3, 4, 3 ] #228 [ 2, 1, 2, 3, 2, 1, 4, 3, 2 ] #229 [ 2, 1, 2, 3, 2, 4, 3, 2, 1 ] #230 [ 2, 3, 2, 1, 4, 3, 2, 1, 2 ] #231 [ 2, 3, 2, 4, 3, 2, 1, 2, 3 ] #232 [ 2, 3, 2, 1, 2, 4, 3, 2, 1 ] #233 [ 2, 1, 3, 4, 3, 2, 1, 2, 3 ] #235 [ 2, 1, 3, 2, 1, 4, 3, 2, 1 ] #236 [ 2, 1, 3, 2, 4, 3, 2, 1, 2 ] #241 [ 1, 2, 1, 4, 3, 2, 1, 2, 3 ] #242 [ 1, 2, 1, 3, 2, 1, 2, 3, 4 ] #243 [ 1, 2, 4, 3, 2, 1, 2, 3, 4 ] #244 [ 1, 3, 2, 1, 2, 3, 4, 3, 2 ] #245 [ 1, 3, 2, 4, 3, 2, 1, 2, 3 ] #248 [ 1, 2, 3, 2, 1, 2, 3, 4, 3 ] #249 [ 1, 3, 2, 1, 4, 3, 2, 1, 2 ] #250 [ 1, 2, 1, 2, 3, 2, 1, 4, 3 ] #251 [ 1, 2, 1, 2, 3, 2, 4, 3, 2 ] #252 [ 1, 2, 1, 3, 2, 1, 4, 3, 2 ] #253 [ 1, 2, 1, 3, 2, 4, 3, 2, 1 ] #256 [ 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #257 [ 1, 2, 3, 2, 1, 2, 4, 3, 2 ] #258 [ 1, 2, 3, 2, 4, 3, 2, 1, 2 ] #259 [ 1, 2, 3, 2, 1, 4, 3, 2, 1 ] #265 [ 3, 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #267 [ 2, 3, 2, 4, 3, 2, 1, 2, 3, 4 ] #268 [ 2, 3, 2, 1, 2, 3, 4, 3, 2, 1 ] #269 [ 2, 1, 3, 4, 3, 2, 1, 2, 3, 4 ] #270 [ 2, 1, 3, 2, 1, 2, 3, 4, 3, 2 ] #271 [ 2, 1, 2, 3, 2, 1, 4, 3, 2, 1 ] #272 [ 2, 1, 2, 3, 2, 4, 3, 2, 1, 2 ] #273 [ 2, 3, 2, 1, 4, 3, 2, 1, 2, 3 ] #275 [ 2, 1, 3, 2, 4, 3, 2, 1, 2, 3 ] #277 [ 2, 1, 3, 2, 1, 4, 3, 2, 1, 2 ] #283 [ 1, 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #284 [ 1, 3, 2, 4, 3, 2, 1, 2, 3, 4 ] #285 [ 1, 3, 2, 1, 2, 3, 4, 3, 2, 1 ] #286 [ 1, 3, 2, 1, 4, 3, 2, 1, 2, 3 ] #287 [ 1, 2, 1, 3, 2, 1, 2, 3, 4, 3 ] #288 [ 1, 2, 3, 4, 3, 2, 1, 2, 3, 4 ] #289 [ 1, 2, 3, 2, 1, 2, 3, 4, 3, 2 ] #290 [ 1, 2, 1, 2, 3, 2, 1, 4, 3, 2 ] #291 [ 1, 2, 1, 2, 3, 2, 4, 3, 2, 1 ] #292 [ 1, 2, 1, 3, 2, 1, 4, 3, 2, 1 ] #293 [ 1, 2, 1, 3, 2, 4, 3, 2, 1, 2 ] #295 [ 1, 2, 1, 3, 4, 3, 2, 1, 2, 3 ] #296 [ 1, 2, 3, 2, 4, 3, 2, 1, 2, 3 ] #297 [ 1, 2, 3, 2, 1, 2, 4, 3, 2, 1 ] #298 [ 1, 2, 3, 2, 1, 4, 3, 2, 1, 2 ] #303 [ 2, 1, 2, 3, 2, 1, 2, 4, 3, 2, 1 ] #305 [ 2, 3, 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #307 [ 2, 1, 3, 2, 4, 3, 2, 1, 2, 3, 4 ] #308 [ 2, 1, 3, 2, 1, 2, 3, 4, 3, 2, 1 ] #309 [ 2, 1, 2, 3, 2, 1, 4, 3, 2, 1, 2 ] #312 [ 2, 1, 3, 2, 1, 4, 3, 2, 1, 2, 3 ] #313 [ 1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2 ] #317 [ 1, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #318 [ 1, 3, 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #320 [ 1, 2, 1, 3, 2, 1, 2, 3, 4, 3, 2 ] #321 [ 1, 2, 1, 3, 4, 3, 2, 1, 2, 3, 4 ] #322 [ 1, 2, 3, 2, 4, 3, 2, 1, 2, 3, 4 ] #323 [ 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1 ] #324 [ 1, 2, 1, 2, 3, 2, 1, 4, 3, 2, 1 ] #325 [ 1, 2, 1, 2, 3, 2, 4, 3, 2, 1, 2 ] #326 [ 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 2 ] #327 [ 1, 2, 1, 3, 2, 4, 3, 2, 1, 2, 3 ] #329 [ 1, 2, 3, 2, 1, 2, 4, 3, 2, 1, 2 ] #330 [ 1, 2, 3, 2, 1, 4, 3, 2, 1, 2, 3 ] #332 [ 2, 1, 2, 3, 2, 1, 2, 4, 3, 2, 1, 2 ] #335 [ 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1 ] #336 [ 2, 1, 2, 3, 2, 1, 4, 3, 2, 1, 2, 3 ] #338 [ 2, 1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2 ] #339 [ 2, 1, 3, 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #341 [ 1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #346 [ 1, 2, 1, 2, 3, 2, 4, 3, 2, 1, 2, 3 ] #347 [ 1, 2, 1, 3, 2, 4, 3, 2, 1, 2, 3, 4 ] #348 [ 1, 2, 1, 3, 2, 1, 2, 3, 4, 3, 2, 1 ] #349 [ 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2 ] #350 [ 1, 2, 3, 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #351 [ 1, 2, 1, 2, 3, 2, 1, 4, 3, 2, 1, 2 ] #352 [ 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 2, 3 ] #354 [ 1, 2, 3, 2, 1, 2, 4, 3, 2, 1, 2, 3 ] #355 [ 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2 ] #356 [ 2, 1, 2, 3, 2, 1, 2, 4, 3, 2, 1, 2, 3 ] #358 [ 2, 1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #359 [ 2, 1, 2, 3, 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #363 [ 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #366 [ 1, 2, 1, 2, 3, 2, 1, 4, 3, 2, 1, 2, 3 ] #367 [ 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 2, 3, 4 ] #368 [ 1, 2, 1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2 ] #369 [ 1, 2, 3, 2, 1, 2, 4, 3, 2, 1, 2, 3, 4 ] #371 [ 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #372 [ 2, 1, 2, 3, 2, 1, 2, 4, 3, 2, 1, 2, 3, 4 ] #376 [ 1, 2, 1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3 ] #380 [ 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4 ] 2.11 = 4211 in family 2.11 = 4211 #18 [ 3, 2, 1 ] #23 [ 2, 1, 3 ] #29 [ 1, 3, 2 ] #30 [ 1, 2, 3 ] #31 [ 3, 2, 1, 2 ] #33 [ 2, 1, 2, 3 ] #39 [ 2, 3, 2, 1 ] #41 [ 2, 1, 3, 2 ] #49 [ 1, 3, 2, 1 ] #51 [ 1, 2, 1, 3 ] #53 [ 1, 2, 3, 2 ] #55 [ 3, 2, 1, 2, 3 ] #56 [ 4, 3, 2, 1, 2 ] #57 [ 3, 2, 1, 2, 4 ] #58 [ 2, 1, 2, 4, 3 ] #59 [ 2, 1, 2, 3, 4 ] #61 [ 2, 1, 2, 3, 2 ] #64 [ 2, 4, 3, 2, 1 ] #65 [ 2, 3, 2, 1, 2 ] #66 [ 2, 1, 3, 2, 1 ] #70 [ 2, 3, 2, 1, 4 ] #79 [ 1, 2, 1, 3, 2 ] #81 [ 1, 2, 4, 3, 2 ] #82 [ 1, 2, 3, 2, 1 ] #86 [ 1, 2, 3, 2, 4 ] #87 [ 4, 3, 2, 1, 2, 3 ] #88 [ 3, 2, 1, 2, 3, 4 ] #89 [ 3, 4, 3, 2, 1, 2 ] #90 [ 3, 2, 1, 2, 4, 3 ] #91 [ 2, 1, 2, 3, 4, 3 ] #92 [ 2, 3, 2, 1, 2, 3 ] #93 [ 2, 1, 2, 3, 2, 1 ] #94 [ 2, 1, 2, 4, 3, 2 ] #95 [ 2, 1, 2, 3, 2, 4 ] #97 [ 3, 2, 1, 4, 3, 2 ] #98 [ 2, 4, 3, 2, 1, 2 ] #103 [ 2, 3, 4, 3, 2, 1 ] #104 [ 2, 3, 2, 1, 2, 4 ] #107 [ 2, 1, 3, 2, 4, 3 ] #117 [ 1, 2, 3, 2, 1, 2 ] #118 [ 1, 2, 4, 3, 2, 1 ] #123 [ 1, 2, 3, 4, 3, 2 ] #124 [ 1, 2, 3, 2, 1, 4 ] #126 [ 4, 3, 2, 1, 2, 3, 4 ] #127 [ 3, 2, 1, 2, 3, 4, 3 ] #128 [ 3, 4, 3, 2, 1, 2, 3 ] #130 [ 3, 2, 1, 2, 4, 3, 2 ] #131 [ 2, 4, 3, 2, 1, 2, 3 ] #132 [ 2, 3, 2, 1, 2, 3, 4 ] #134 [ 2, 1, 2, 4, 3, 2, 1 ] #135 [ 2, 1, 2, 3, 2, 1, 4 ] #136 [ 2, 1, 2, 3, 4, 3, 2 ] #137 [ 3, 2, 4, 3, 2, 1, 2 ] #138 [ 3, 2, 1, 4, 3, 2, 1 ] #140 [ 2, 1, 2, 3, 2, 4, 3 ] #143 [ 2, 3, 4, 3, 2, 1, 2 ] #144 [ 2, 3, 2, 1, 2, 4, 3 ] #147 [ 2, 1, 3, 2, 1, 4, 3 ] #160 [ 1, 2, 4, 3, 2, 1, 2 ] #162 [ 1, 3, 2, 1, 4, 3, 2 ] #163 [ 1, 2, 1, 3, 2, 4, 3 ] #166 [ 1, 2, 3, 2, 1, 2, 4 ] #167 [ 1, 2, 3, 4, 3, 2, 1 ] #170 [ 3, 4, 3, 2, 1, 2, 3, 4 ] #174 [ 3, 2, 1, 2, 3, 4, 3, 2 ] #175 [ 3, 2, 4, 3, 2, 1, 2, 3 ] #176 [ 3, 2, 1, 2, 4, 3, 2, 1 ] #177 [ 2, 4, 3, 2, 1, 2, 3, 4 ] #180 [ 2, 1, 2, 3, 4, 3, 2, 1 ] #182 [ 2, 3, 2, 1, 2, 3, 4, 3 ] #188 [ 2, 3, 4, 3, 2, 1, 2, 3 ] #191 [ 2, 1, 3, 2, 1, 4, 3, 2 ] #206 [ 1, 3, 2, 1, 4, 3, 2, 1 ] #208 [ 1, 2, 1, 3, 2, 1, 4, 3 ] #212 [ 1, 2, 3, 4, 3, 2, 1, 2 ] #213 [ 1, 2, 3, 2, 1, 2, 4, 3 ] #221 [ 3, 2, 4, 3, 2, 1, 2, 3, 4 ] #222 [ 3, 2, 1, 2, 3, 4, 3, 2, 1 ] #226 [ 2, 3, 4, 3, 2, 1, 2, 3, 4 ] #235 [ 2, 1, 3, 2, 1, 4, 3, 2, 1 ] #252 [ 1, 2, 1, 3, 2, 1, 4, 3, 2 ] #256 [ 1, 2, 3, 4, 3, 2, 1, 2, 3 ] 11.11 = 2222 in family 11.11 = 2222 #32 [ 2, 1, 2, 4 ] #56 [ 4, 3, 2, 1, 2 ] #57 [ 3, 2, 1, 2, 4 ] #58 [ 2, 1, 2, 4, 3 ] #59 [ 2, 1, 2, 3, 4 ] #90 [ 3, 2, 1, 2, 4, 3 ] 1.111 = 221111 in family 1.111 = 221111 #16 [ 2, 1, 2 ] #31 [ 3, 2, 1, 2 ] #33 [ 2, 1, 2, 3 ] #55 [ 3, 2, 1, 2, 3 ] #87 [ 4, 3, 2, 1, 2, 3 ] #88 [ 3, 2, 1, 2, 3, 4 ] #126 [ 4, 3, 2, 1, 2, 3, 4 ]