cp's OEIS Frontend

A335514 Number of (1,2,3)-matching compositions of n.

%I A335514 #10 Dec 31 2020 15:36:49
%S A335514 0,0,0,0,0,0,1,4,14,42,114,292,714,1686,3871,8696,19178,41667,89386,
%T A335514 189739,399144,833290,1728374,3565148,7319212,14965880,30496302,
%U A335514 61961380,125577752,253971555,512716564,1033496947,2080572090,4183940550,8406047907,16875834728
%N A335514 Number of (1,2,3)-matching compositions of n.
%H A335514 Andrew Howroyd, <a href="/A335514/b335514.txt">Table of n, a(n) for n = 0..500</a>
%H A335514 Gus Wiseman, <a href="/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%F A335514 a(n > 0) = 2^(n - 1) - A102726(n).
%e A335514 The a(6) = 1 through a(8) = 14 compositions:
%e A335514   (1,2,3)  (1,2,4)    (1,2,5)
%e A335514            (1,1,2,3)  (1,3,4)
%e A335514            (1,2,1,3)  (1,1,2,4)
%e A335514            (1,2,3,1)  (1,2,1,4)
%e A335514                       (1,2,2,3)
%e A335514                       (1,2,3,2)
%e A335514                       (1,2,4,1)
%e A335514                       (2,1,2,3)
%e A335514                       (1,1,1,2,3)
%e A335514                       (1,1,2,1,3)
%e A335514                       (1,1,2,3,1)
%e A335514                       (1,2,1,1,3)
%e A335514                       (1,2,1,3,1)
%e A335514                       (1,2,3,1,1)
%t A335514 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],MatchQ[#,{___,x_,___,y_,___,z_,___}/;x<y<z]&]],{n,0,10}]
%Y A335514 The version for permutations is A056986.
%Y A335514 The avoiding version is A102726.
%Y A335514 These compositions are ranked by A335479.
%Y A335514 The version for patterns is A335515.
%Y A335514 The version for prime indices is A335520.
%Y A335514 Permutations are counted by A000142 and ranked by A333218.
%Y A335514 Patterns are counted by A000670 and ranked by A333217.
%Y A335514 Patterns matched by compositions are counted by A335456.
%Y A335514 Cf. A011782, A032020, A106356, A226316, A269134, A333755, A335465, A335521.
%K A335514 nonn
%O A335514 0,8
%A A335514 _Gus Wiseman_, Jun 22 2020
%E A335514 Terms a(21) and beyond from _Andrew Howroyd_, Dec 31 2020