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A117957
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Number of partitions of n into parts larger than 1 and congruent to 1 mod 4.
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0
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1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 2, 1, 2, 3, 3, 2, 2, 4, 4, 3, 3, 5, 6, 5, 4, 6, 8, 7, 6, 8, 10, 10, 9, 10, 13, 13, 12, 14, 17, 18, 16, 18, 22, 23, 22, 23, 28, 31, 29, 30, 36, 39, 39, 39, 45, 51, 50, 51, 57, 64, 65, 65, 73, 81, 83, 84, 91, 102, 106, 106
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OFFSET
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0,19
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COMMENTS
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Also number of partitions of n such that 2k and 2k+1 occur with the same multiplicities. Example: a(26)=3 because we have [11,10,3,2], [9,8,5,4] and [7,7,6,6]. It is easy to find a bijection between these partitions and those described in the definition.
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LINKS
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Table of n, a(n) for n=0..82.
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FORMULA
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G.f.=1/product(1-x^(4i+1), i=1..infinity).
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EXAMPLE
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a(26)=3 because we have [21,5],[17,9] and [13,13].
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MAPLE
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g:=1/product(1-x^(4*i+1), i=1..50): gser:=series(g, x=0, 93): seq(coeff(gser, x, n), n=0..88);
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CROSSREFS
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Cf. A035451, A035462.
Sequence in context: A086995 A220492 A135230 * A139632 A145704 A145705
Adjacent sequences: A117954 A117955 A117956 * A117958 A117959 A117960
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Apr 05 2006
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STATUS
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approved
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