cp's OEIS Frontend

A344614 Number of compositions of n with no adjacent triples (..., x, y, z, ...) where x < y < z or x > y > z.

%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