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A357182
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Number of integer compositions of n with the same length as their alternating sum.
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26
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1, 1, 0, 0, 1, 3, 1, 4, 6, 20, 13, 48, 50, 175, 141, 512, 481, 1719, 1491, 5400, 4929, 17776, 15840, 57420, 52079, 188656, 169989, 617176, 559834, 2033175, 1842041, 6697744, 6085950, 22139780, 20123989, 73262232, 66697354, 242931321, 221314299, 806516560
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OFFSET
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0,6
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COMMENTS
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A composition of n is a finite sequence of positive integers summing to n.
The alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(i-1) y_i.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(8) = 6 compositions:
(1) (31) (113) (42) (124) (53)
(212) (223) (1151)
(311) (322) (2141)
(421) (3131)
(4121)
(5111)
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MATHEMATICA
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ats[y_]:=Sum[(-1)^(i-1)*y[[i]], {i, Length[y]}];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Length[#]==ats[#]&]], {n, 0, 15}]
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CROSSREFS
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For product instead of length we have A114220.
For sum equal to twice alternating sum we have A262977, ranked by A348614.
For absolute value we have A357183.
These compositions are ranked by A357184.
A124754 gives alternating sums of standard compositions.
A238279 counts compositions by sum and number of maximal runs.
A261983 counts non-anti-run compositions.
A357136 counts compositions by alternating sum.
Cf. A000120, A032020, A070939, A106356, A114901, A131044, A178470, A233564, A242882, A262046, A301987.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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