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A357189
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Number of integer partitions of n with the same length as alternating sum.
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25
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1, 1, 0, 0, 1, 1, 1, 2, 2, 4, 3, 5, 6, 9, 9, 13, 16, 23, 23, 34, 37, 54, 54, 78, 84, 120, 121, 170, 182, 252, 260, 358, 379, 517, 535, 725, 764, 1030, 1064, 1427, 1494, 1992, 2059, 2733, 2848, 3759, 3887, 5106, 5311, 6946, 7177, 9345, 9701, 12577, 12996, 16788
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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 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(4) = 1 through a(13) = 9 partitions:
31 311 42 322 53 333 64 443 75 553
421 5111 432 5221 542 5331 652
531 6211 641 6222 751
51111 52211 6321 52222
62111 7311 53311
711111 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[#]&]], {n, 0, 30}]
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CROSSREFS
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For sum equal to twice alternating sum we have A357189 (this sequence).
These partitions are ranked by A357486.
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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