This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344614 #14 Jun 12 2021 06:05:12 %S A344614 1,1,2,4,8,16,30,58,110,209,397,753,1429,2711,5143,9757,18511,35117, %T A344614 66621,126389,239781,454897,863010,1637260,3106138,5892821,11179603, %U A344614 21209446,40237641,76337091,144823431,274752731,521249018,988891100,1876081530,3559220898,6752400377 %N A344614 Number of compositions of n with no adjacent triples (..., x, y, z, ...) where x < y < z or x > y > z. %C A344614 These compositions avoid the strict consecutive patterns (1,2,3) and (3,2,1), the weak version being A344604. %e A344614 The a(6) = 30 compositions are: %e A344614 (6) (15) (114) (1113) (11112) (111111) %e A344614 (24) (132) (1122) (11121) %e A344614 (33) (141) (1131) (11211) %e A344614 (42) (213) (1212) (12111) %e A344614 (51) (222) (1221) (21111) %e A344614 (231) (1311) %e A344614 (312) (2112) %e A344614 (411) (2121) %e A344614 (2211) %e A344614 (3111) %e A344614 Missing are: (123), (321). %t A344614 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MatchQ[#,{___,x_,y_,z_,___}/;x<y<z||x>y>z]&]],{n,0,15}] %Y A344614 A001250 counts alternating permutations. %Y A344614 A005649 counts anti-run patterns. %Y A344614 A025047 counts wiggly compositions (ascend: A025048, descend: A025049). %Y A344614 A106356 counts compositions by number of maximal anti-runs. %Y A344614 A114901 counts compositions where each part is adjacent to an equal part. %Y A344614 A325534 counts separable partitions. %Y A344614 A325535 counts inseparable partitions. %Y A344614 A344604 counts wiggly compositions with twins. %Y A344614 A344605 counts wiggly patterns with twins. %Y A344614 A344606 counts wiggly permutations of prime factors with twins. %Y A344614 Counting compositions by patterns: %Y A344614 - A003242 avoiding (1,1) adjacent. %Y A344614 - A011782 no conditions. %Y A344614 - A106351 avoiding (1,1) adjacent by sum and length. %Y A344614 - A128695 avoiding (1,1,1) adjacent. %Y A344614 - A128761 avoiding (1,2,3). %Y A344614 - A232432 avoiding (1,1,1). %Y A344614 - A335456 all patterns. %Y A344614 - A335457 all patterns adjacent. %Y A344614 - A335514 matching (1,2,3). %Y A344614 - A344604 weakly avoiding (1,2,3) and (3,2,1) adjacent. %Y A344614 - A344614 avoiding (1,2,3) and (3,2,1) adjacent. %Y A344614 - A344615 weakly avoiding (1,2,3) adjacent. %Y A344614 Cf. A000041, A006330, A008965, A049774, A056986, A238279/A333755, A333213, A335515, A344612, A344652. %K A344614 nonn %O A344614 0,3 %A A344614 _Gus Wiseman_, May 27 2021 %E A344614 More terms from _Bert Dobbelaere_, Jun 12 2021