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Search: id:A116458
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| A116458 |
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Number of partitions of n into parts congruent to 1, 9, or 11 (mod 14). |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 14, 15, 16, 17, 19, 21, 22, 24, 26, 29, 31, 34, 36, 38, 41, 44, 48, 51, 55, 60, 64, 68, 73, 79, 84, 91, 97, 103, 110, 117, 125, 133, 142, 152, 163, 172, 183, 196, 208, 222, 236, 250, 265, 281
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OFFSET
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0,10
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COMMENT
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Also number of partitions of n into distinct parts congruent to 1,2, or 4 (mod 7). Example: a(15)=4 because we have [15],[11,4],[9,4,2], and [8,4,2,1].
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REFERENCES
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G. E. Andrews, Number Theory, Dover Publications, 1994 (p. 166, Exercise 7).
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FORMULA
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G.f.=1/product((1-x^(1+14j))(1-x^(9+14j))(1-x^(11+14j)),j=0..infinity). G.f.=product((1+x^(1+7j))(1+x^(2+7j))(1+x^(4+7j)),j=0..infinity).
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EXAMPLE
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a(15)=4 because we have [15],[11,1,1,1,1],[9,1,1,1,1,1,1], and [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1].
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MAPLE
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g:=product((1+x^(1+7*j))*(1+x^(2+7*j))*(1+x^(4+7*j)), j=0..15): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=0..77);
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CROSSREFS
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Sequence in context: A107320 A095186 A101402 this_sequence A093875 A114214 A074198
Adjacent sequences: A116455 A116456 A116457 this_sequence A116459 A116460 A116461
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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), Feb 16 2006
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