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A374703
Number of integer compositions of 2n whose leaders of weakly decreasing runs sum to n. Center n = 2*k of the triangle A374748.
2
1, 1, 2, 9, 24, 96, 343, 1242, 4700, 17352, 65995
OFFSET
0,3
COMMENTS
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.
EXAMPLE
The a(0) = 1 through a(4) = 24 compositions:
() (11) (22) (33) (44)
(211) (321) (422)
(1122) (431)
(1221) (1133)
(3111) (1322)
(11112) (1331)
(11121) (4211)
(11211) (11132)
(12111) (11321)
(13211)
(21122)
(21221)
(22112)
(22121)
(41111)
(111113)
(111131)
(111311)
(113111)
(131111)
(211112)
(211121)
(211211)
(212111)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[2n], Total[First/@Split[#, GreaterEqual]]==n&]], {n, 0, 8}]
CROSSREFS
For reversed partitions we have A364910.
For strictly decreasing runs we have the center of A374700.
Center n = 2*k of the triangle A374748.
A003242 counts anti-run compositions.
A011782 counts integer compositions.
A238130, A238279, A333755 count compositions by number of runs.
A274174 counts contiguous compositions, ranks A374249.
Sequence in context: A143561 A363660 A027302 * A213720 A353822 A073981
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 12 2024
STATUS
approved