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Search: id:A089958
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| A089958 |
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Number of partitions of n in which every part occurs 2, 3, or 5 times. |
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+0
2
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| 1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 4, 4, 8, 5, 9, 11, 11, 12, 20, 15, 23, 27, 28, 31, 45, 38, 52, 61, 64, 71, 96, 87, 112, 129, 136, 151, 194, 184, 227, 259, 275, 304, 376, 368, 441, 499, 531, 586, 704, 705, 826, 927, 989, 1088, 1280, 1302, 1500, 1672, 1787, 1960, 2267
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Also number of partitions of n in which every part is congruent to {2, 3, 6, 9, 10} mod 12. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 07 2005
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REFERENCES
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M. V. Subbarao, Combinatorial proofs of some identities, Proc. Washington State Univ. Conf. Number Theory, 1971, pp. 80-91.
M. V. Subbarao, On a partition theorem of Mac Mahon-Andrews, Proc. Amer. Math. Soc., 27, 1971, 449-450.
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LINKS
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Eric Weisstein's World of Mathematics, Partition Function P
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FORMULA
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Euler transform of period 12 sequence [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, ...]. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 07 2005
Expansion of q^(-5/24)eta(q^6)eta(q^4)/(eta(q^2)eta(q^3)) in powers of q.
G.f.=product(1+x^(2j)+x^(3j)+x^(5j), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2006
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EXAMPLE
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a(11)=4 because we have [4,4,1,1,1],[3,3,3,1,1],[3,3,1,1,1,1,1] and [2,2,2,1,1,1,1,1].
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MAPLE
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g:=product(1+x^(2*j)+x^(3*j)+x^(5*j), j=1..50): gser:=series(g, x=0, 63): seq(coeff(gser, x, n), n=0..60); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2006
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^4+A)*eta(x^6+A)/eta(x^2+A)/eta(x^3+A), n))} /* Michael Somos Jan 19 2005 */
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CROSSREFS
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Sequence in context: A081772 A050121 A029152 this_sequence A162932 A008924 A021323
Adjacent sequences: A089955 A089956 A089957 this_sequence A089959 A089960 A089961
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Nov 16, 2003
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