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A363626
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Number of integer compositions of n with weighted alternating sum 0.
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9
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1, 0, 0, 1, 1, 0, 2, 5, 7, 8, 14, 38, 64, 87, 174, 373, 649, 1069, 2051, 4091, 7453, 13276, 25260, 48990, 91378, 168890, 321661, 618323, 1169126, 2203649, 4211163, 8085240, 15421171, 29390131, 56382040, 108443047, 208077560, 399310778
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OFFSET
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0,7
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COMMENTS
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We define the weighted alternating sum of a sequence (y_1,...,y_k) to be Sum_{i=1..k} (-1)^(i-1) * i * y_i.
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LINKS
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EXAMPLE
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The a(3) = 1 through a(10) = 14 compositions:
(21) (121) . (42) (331) (242) (63) (541)
(3111) (1132) (1331) (153) (2143)
(2221) (11132) (4122) (3232)
(21121) (12221) (5211) (4321)
(112111) (23111) (13122) (15112)
(121121) (14211) (31231)
(1112111) (411111) (42121)
(1311111) (114112)
(212122)
(213211)
(311221)
(322111)
(3111121)
(21211111)
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MATHEMATICA
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altwtsum[y_]:=Sum[(-1)^(k-1)*k*y[[k]], {k, 1, Length[y]}];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], altwtsum[#]==0&]], {n, 0, 10}]
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CROSSREFS
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A363619 gives weighted alternating sum of prime indices, reverse A363620.
A363624 gives weighted alternating sum of Heinz partition, reverse A363625.
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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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