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A357487
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Number of integer partitions of n with the same length as reverse-alternating sum.
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11
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1, 1, 0, 0, 0, 1, 0, 2, 0, 4, 0, 5, 0, 9, 0, 13, 0, 23, 0, 34, 0, 54, 0, 78, 0, 120, 0, 170, 0, 252, 0, 358, 0, 517, 0, 725, 0, 1030, 0, 1427, 0, 1992, 0, 2733, 0, 3759, 0, 5106, 0, 6946, 0, 9345, 0, 12577, 0, 16788, 0, 22384, 0, 29641, 0
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OFFSET
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0,8
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COMMENTS
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A partition of n is a weakly decreasing sequence of positive integers summing to n.
The reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^i y_i.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(13) = 9 partitions:
1 . . . 311 . 322 . 333 . 443 . 553
421 432 542 652
531 641 751
51111 52211 52222
62111 53311
62221
63211
73111
7111111
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MATHEMATICA
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ats[y_]:=Sum[(-1)^(i-1)*y[[i]], {i, Length[y]}];
Table[Length[Select[IntegerPartitions[n], Length[#]==ats[Reverse[#]]&]], {n, 0, 30}]
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CROSSREFS
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These partitions are ranked by A357485.
A025047 counts alternating compositions.
A357136 counts compositions by alternating sum, full triangle A097805.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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