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Search: id:A117956
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| A117956 |
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Number of partitions of n into exactly 2 types of parts: one odd and one even. |
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+0
1
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| 0, 0, 1, 1, 4, 3, 8, 6, 13, 10, 19, 13, 26, 20, 32, 23, 41, 31, 49, 34, 58, 45, 66, 47, 76, 60, 88, 60, 96, 76, 106, 76, 122, 93, 126, 94, 140, 111, 158, 106, 163, 134, 175, 127, 196, 150, 198, 149, 212, 170, 240, 164, 238, 200, 250, 180, 284, 214, 277, 216, 292, 238
(list; graph; listen)
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OFFSET
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1,5
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FORMULA
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G.f.=sum(sum(x^(2i+2j-2)/[(1-x^(2i-1))(1-x^(2j-1))], j=1..i-1), i=1..infinity).
Convolution of x(n) and y(n), where x(n) is the number of even divisors of n and y(n) is the number of odd divisors of n. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 05 2006
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EXAMPLE
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a(7)=8 because we have [6,1],[5,2],[4,3],[4,1,1,1],[3,2,2],[2,2,2,1],[2,2,1,1,1], and [2,1,1,1,1,1].
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MAPLE
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g:=sum(sum(x^(2*i+2*j-1)/(1-x^(2*i-1))/(1-x^(2*j)), j=1..40), i=1..40): gser:=series(g, x=0, 70): seq(coeff(gser, x^n), n=1..67);
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CROSSREFS
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Cf. A002133, A117955.
Sequence in context: A007015 A114562 A011451 this_sequence A110662 A132021 A089368
Adjacent sequences: A117953 A117954 A117955 this_sequence A117957 A117958 A117959
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 05 2006
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