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Search: id:A108932
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| A108932 |
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Number of partitions of n into parts that are congruent to 1, 5 or 6 mod 8. |
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1
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| 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 6, 7, 8, 10, 12, 13, 15, 18, 21, 24, 27, 31, 36, 41, 46, 52, 60, 68, 76, 86, 97, 109, 122, 136, 153, 172, 191, 212, 237, 264, 293, 325, 360, 400, 443, 488, 539, 596, 657, 723, 796, 876, 963, 1057, 1159, 1272, 1395, 1526, 1669, 1827
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Number of partitions of n into distinct parts that are not congruent to 3 mod 4, and the number of partitions of n into odd parts such that each part which is congruent to 3 mod 4 occurs an even number of times.
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FORMULA
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G.f.: prod_{k >= 0} 1/{(1 - x^{8k + 1})(1 - x^{8k + 5})(1 - x^{8k + 6})}
Euler transform of period 8 sequence [1, 0, 0, 0, 1, 1, 0, 0, ...]. - Michael Somos, Jul 29 2005
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PROGRAM
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(PARI) {a(n)=if(n< 0, 0, polcoeff( 1/prod(k=1, n, 1-[0, 1, 0, 0, 0, 1, 1, 0][k%8+1]*x^k, 1+x*O(x^n)), n))} /* Michael Somos Jul 29 2005 */
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CROSSREFS
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Adjacent sequences: A108929 A108930 A108931 this_sequence A108933 A108934 A108935
Sequence in context: A076896 A029087 A029068 this_sequence A029067 A048460 A036017
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KEYWORD
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nonn
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AUTHOR
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Naoki Sato (nsato7(AT)yahoo.ca), Jul 20 2005
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