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A375297 Number of integer compositions of n matching both of the dashed patterns 23-1 and 1-32.

%I A375297 #5 Aug 27 2024 09:14:32
%S A375297 0,0,0,0,0,0,0,0,0,1,6,21,68,199,545,1410,3530,8557,20255,46968,
%T A375297 107135,240927,535379,1177435,2566618,5551456
%N A375297 Number of integer compositions of n matching both of the dashed patterns 23-1 and 1-32.
%C A375297 Also the number of integer compositions of n whose leaders of maximal weakly increasing runs are not weakly decreasing and whose reverse satisfies the same condition.
%H A375297 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>.
%H A375297 Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.
%e A375297 The a(0) = 0 through a(11) = 21 compositions:
%e A375297   .  .  .  .  .  .  .  .  .  (12321)  (1342)    (1352)
%e A375297                                       (2431)    (2531)
%e A375297                                       (12421)   (11342)
%e A375297                                       (13231)   (12431)
%e A375297                                       (112321)  (12521)
%e A375297                                       (123211)  (13241)
%e A375297                                                 (13421)
%e A375297                                                 (14231)
%e A375297                                                 (23132)
%e A375297                                                 (24311)
%e A375297                                                 (112421)
%e A375297                                                 (113231)
%e A375297                                                 (122321)
%e A375297                                                 (123212)
%e A375297                                                 (123221)
%e A375297                                                 (124211)
%e A375297                                                 (132311)
%e A375297                                                 (212321)
%e A375297                                                 (1112321)
%e A375297                                                 (1123211)
%e A375297                                                 (1232111)
%t A375297 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], MatchQ[#,{___,y_,z_,___,x_,___}/;x<y<z]&&MatchQ[#,{___,x_,___,z_,y_,___}/;x<y<z]&]],{n,0,15}]
%Y A375297 For leaders of identical runs we have A332834.
%Y A375297 For just one of the two conditions we have A374636, ranks A375137/A375138.
%Y A375297 These compositions are ranked by A375407.
%Y A375297 A003242 counts anti-runs, ranks A333489.
%Y A375297 A011782 counts compositions.
%Y A375297 A106356 counts compositions by number of maximal anti-runs.
%Y A375297 A238130, A238279, A333755 count compositions by number of runs.
%Y A375297 A274174 counts contiguous compositions, ranks A374249.
%Y A375297 A335456 counts patterns matched by compositions.
%Y A375297 Cf. A000041, A056823, A188920, A189076, A238343, A333213, A335514, A374631, A374632, A374635, A374681.
%K A375297 nonn,more
%O A375297 0,11
%A A375297 _Gus Wiseman_, Aug 23 2024