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Search: id:A116634
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| A116634 |
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Number of partitions of n having exactly one part that is a multiple of 3. |
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+0
2
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| 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 14, 20, 26, 36, 47, 62, 80, 104, 132, 169, 212, 267, 332, 414, 510, 629, 769, 941, 1142, 1386, 1672, 2016, 2417, 2897, 3455, 4118, 4888, 5796, 6849, 8085, 9513, 11182, 13107, 15347, 17923, 20910, 24338, 28298, 32833, 38054, 44021
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Column 1 of A116633.
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FORMULA
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G.f.=x^3/[(1-x^3)product((1-x^(3j-2))(1-x^(3j-1)), j=1..infinity)].
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EXAMPLE
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a(7)=5 because we have [6,1],[4,3],[3,2,2],[3,2,1,1] and [3,1,1,1,1].
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MAPLE
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g:=x^3/(1-x^3)/product((1-x^(3*j-2))*(1-x^(3*j-1)), j=1..30): gser:=series(g, x=0, 56): seq(coeff(gser, x, n), n=0..53);
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CROSSREFS
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Cf. A116633, A000726.
Sequence in context: A001522 A054405 A155167 this_sequence A035960 A023893 A065094
Adjacent sequences: A116631 A116632 A116633 this_sequence A116635 A116636 A116637
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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 19 2006
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