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A357640
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Number of reversed integer partitions of 2n whose skew-alternating sum is 0.
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22
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1, 1, 2, 3, 6, 9, 16, 24, 40, 59, 93, 136, 208, 299, 445, 632, 921, 1292, 1848, 2563, 3610, 4954, 6881, 9353, 12835, 17290, 23469, 31357, 42150, 55889, 74463, 98038, 129573, 169476, 222339, 289029, 376618, 486773, 630313, 810285, 1043123, 1334174
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OFFSET
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0,3
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COMMENTS
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We define the skew-alternating sum of a sequence (A, B, C, D, E, F, G, ...) to be A - B - C + D + E - F - G + ...
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LINKS
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EXAMPLE
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The a(0) = 1 through a(5) = 9 partitions:
() (11) (22) (33) (44) (55)
(1111) (2211) (2222) (3322)
(111111) (3221) (4321)
(3311) (4411)
(221111) (222211)
(11111111) (322111)
(331111)
(22111111)
(1111111111)
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MATHEMATICA
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skats[f_]:=Sum[f[[i]]*(-1)^(1+Ceiling[(i+1)/2]), {i, Length[f]}];
Table[Length[Select[IntegerPartitions[2n], skats[Reverse[#]]==0&]], {n, 0, 15}]
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CROSSREFS
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The half-alternating version is A357639.
A000041 counts integer partitions (also reversed integer partitions).
A344651 counts alternating sum of partitions by length, ordered A097805.
A351005 = alternately equal and unequal partitions, compositions A357643.
A351006 = alternately unequal and equal partitions, compositions A357644.
A357621 gives half-alternating sum of standard compositions, skew A357623.
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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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