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Search: id:A090794
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| A090794 |
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Number of partitions of n such that the set of parts has an odd number of elements. |
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3
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| 1, 2, 2, 3, 2, 5, 4, 9, 13, 19, 27, 43, 54, 71, 102, 124, 161, 200, 257, 319, 400, 484, 618, 761, 956, 1164, 1450, 1806, 2226, 2741, 3367, 4137, 5020, 6163, 7485, 9042, 10903, 13172, 15721, 18956, 22542, 26925, 31935, 37962, 44861, 53183, 62651
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = b(n, 1, 0, 0) with b(n, i, j, f) = if i<n then b(n-i, i, i, 1-f-(1-2*f)*0^(i-j)) + b(n, i+1, j, f) else (1-f-(1-2*f)*0^(i-j))*0^(i-n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 19 2004
G.f.: F(x)*G(x)/2, where F(x) = 1-Product(1-2*x^i, i=1..infinity) and G(x) = 1/Product(1-x^i, i=1..infinity).
a(n) = (A000041(n)-A104575(n))/2.
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EXAMPLE
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n=6 has A000041(6)=11 partitions: 6, 5+1, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, and 1+1+1+1+1+1 with partition sets: {6}, {1,5}, {2,4}, {1,4}, {3}, {1,2,3}, {1,3}, {2}, {1,2}, {1,2}, and {1}, five of them have an odd number of elements, therefore a(6)=5.
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CROSSREFS
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Cf. A060177, A002134, A000005, A027193, A090794.
Cf. also A092314, A092322, A092269, A092309, A092321, A092313, A092310, A092311, A092268
Cf. A092306.
Sequence in context: A065769 A113298 A058705 this_sequence A050323 A015995 A068903
Adjacent sequences: A090791 A090792 A090793 this_sequence A090795 A090796 A090797
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 12 2004
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EXTENSIONS
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More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 17 2004
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