cp's OEIS Frontend

A344615 Number of compositions of n with no adjacent triples (..., x, y, z, ...) where x <= y <= z.

%I A344615 #10 Jun 12 2021 06:05:07
%S A344615 1,1,2,3,6,10,17,29,50,84,143,241,408,688,1162,1959,3305,5571,9393,
%T A344615 15832,26688,44980,75812,127769,215338,362911,611620,1030758,1737131,
%U A344615 2927556,4933760,8314754,14012668,23615198,39798098,67070686,113032453,190490542,321028554
%N A344615 Number of compositions of n with no adjacent triples (..., x, y, z, ...) where x <= y <= z.
%C A344615 These compositions avoid the weak consecutive pattern (1,2,3), the strict version being A128761.
%e A344615 The a(1) = 1 through a(6) = 17 compositions:
%e A344615   (1)  (2)    (3)    (4)      (5)        (6)
%e A344615        (1,1)  (1,2)  (1,3)    (1,4)      (1,5)
%e A344615               (2,1)  (2,2)    (2,3)      (2,4)
%e A344615                      (3,1)    (3,2)      (3,3)
%e A344615                      (1,2,1)  (4,1)      (4,2)
%e A344615                      (2,1,1)  (1,3,1)    (5,1)
%e A344615                               (2,1,2)    (1,3,2)
%e A344615                               (2,2,1)    (1,4,1)
%e A344615                               (3,1,1)    (2,1,3)
%e A344615                               (1,2,1,1)  (2,3,1)
%e A344615                                          (3,1,2)
%e A344615                                          (3,2,1)
%e A344615                                          (4,1,1)
%e A344615                                          (1,2,1,2)
%e A344615                                          (1,3,1,1)
%e A344615                                          (2,1,2,1)
%e A344615                                          (2,2,1,1)
%t A344615 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MatchQ[#,{___,x_,y_,z_,___}/;x<=y<=z]&]],{n,0,15}]
%Y A344615 The case of permutations is A049774.
%Y A344615 The strict non-adjacent version is A102726.
%Y A344615 The case of permutations of prime indices is A344652.
%Y A344615 A001250 counts alternating permutations.
%Y A344615 A005649 counts anti-run patterns.
%Y A344615 A106356 counts compositions by number of maximal anti-runs.
%Y A344615 A114901 counts compositions where each part is adjacent to an equal part.
%Y A344615 A344604 counts wiggly compositions with twins.
%Y A344615 A344605 counts wiggly patterns with twins.
%Y A344615 A344606 counts wiggly permutations of prime factors with twins.
%Y A344615 Counting compositions by patterns:
%Y A344615 - A003242 avoiding (1,1) adjacent.
%Y A344615 - A011782 no conditions.
%Y A344615 - A106351 avoiding (1,1) adjacent by sum and length.
%Y A344615 - A128695 avoiding (1,1,1) adjacent.
%Y A344615 - A128761 avoiding (1,2,3).
%Y A344615 - A232432 avoiding (1,1,1).
%Y A344615 - A335456 all patterns.
%Y A344615 - A335457 all patterns adjacent.
%Y A344615 - A335514 matching (1,2,3).
%Y A344615 - A344604 weakly avoiding (1,2,3) and (3,2,1) adjacent.
%Y A344615 - A344614 avoiding (1,2,3) and (3,2,1) adjacent.
%Y A344615 - A344615 weakly avoiding (1,2,3) adjacent.
%Y A344615 Cf. A000041, A006330, A008965, A027187, A238279/A333755, A333213, A335464, A335515, A344612, A344619.
%K A344615 nonn
%O A344615 0,3
%A A344615 _Gus Wiseman_, May 27 2021
%E A344615 More terms from _Bert Dobbelaere_, Jun 12 2021