cp's OEIS Frontend

A374703 Number of integer compositions of 2n whose leaders of weakly decreasing runs sum to n. Center n = 2*k of the triangle A374748.

%I A374703 #5 Aug 13 2024 09:10:09
%S A374703 1,1,2,9,24,96,343,1242,4700,17352,65995
%N A374703 Number of integer compositions of 2n whose leaders of weakly decreasing runs sum to n. Center n = 2*k of the triangle A374748.
%C A374703 The weakly decreasing run-leaders of a sequence are obtained by splitting it into maximal weakly decreasing subsequences and taking the first term of each.
%H A374703 Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.
%e A374703 The a(0) = 1 through a(4) = 24 compositions:
%e A374703   ()  (11)  (22)   (33)     (44)
%e A374703             (211)  (321)    (422)
%e A374703                    (1122)   (431)
%e A374703                    (1221)   (1133)
%e A374703                    (3111)   (1322)
%e A374703                    (11112)  (1331)
%e A374703                    (11121)  (4211)
%e A374703                    (11211)  (11132)
%e A374703                    (12111)  (11321)
%e A374703                             (13211)
%e A374703                             (21122)
%e A374703                             (21221)
%e A374703                             (22112)
%e A374703                             (22121)
%e A374703                             (41111)
%e A374703                             (111113)
%e A374703                             (111131)
%e A374703                             (111311)
%e A374703                             (113111)
%e A374703                             (131111)
%e A374703                             (211112)
%e A374703                             (211121)
%e A374703                             (211211)
%e A374703                             (212111)
%t A374703 Table[Length[Select[Join@@Permutations /@ IntegerPartitions[2n],Total[First/@Split[#,GreaterEqual]]==n&]],{n,0,8}]
%Y A374703 For reversed partitions we have A364910.
%Y A374703 For strictly decreasing runs we have the center of A374700.
%Y A374703 Center n = 2*k of the triangle A374748.
%Y A374703 A003242 counts anti-run compositions.
%Y A374703 A011782 counts integer compositions.
%Y A374703 A238130, A238279, A333755 count compositions by number of runs.
%Y A374703 A274174 counts contiguous compositions, ranks A374249.
%Y A374703 Cf. A000041, A004526, A106356, A124766, A188900, A238343, A261982, A333213.
%K A374703 nonn,more
%O A374703 0,3
%A A374703 _Gus Wiseman_, Aug 12 2024