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Search: id:A116635
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| A116635 |
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Number of parts that are multiples of 3 in all partitions of n. |
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+0
2
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| 0, 0, 0, 1, 1, 2, 5, 7, 11, 19, 27, 40, 61, 85, 120, 170, 232, 316, 433, 576, 767, 1017, 1332, 1735, 2259, 2905, 3730, 4768, 6058, 7663, 9676, 12137, 15191, 18945, 23541, 29150, 36026, 44336, 54453, 66686, 81456, 99227, 120653, 146275, 177015, 213724
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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a(n)=Sum(A116633(n,k),k=0..floor(n/3)).
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FORMULA
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G.f.=sum(x^(3i)/(1-x^(3i)), i=1..infinity)/product(1-x^j, j=1..infinity).
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EXAMPLE
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a(6)=5 because in the 11 partitions of 6, namely, [(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], we have 5 multiples of 3 (shown between parentheses).
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MAPLE
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g:=sum(x^(3*i)/(1-x^(3*i)), i=1..50)/product(1-x^j, j=1..50): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=0..52);
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CROSSREFS
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Cf. A116633.
Sequence in context: A045350 A045351 A051645 this_sequence A038884 A040122 A038955
Adjacent sequences: A116632 A116633 A116634 this_sequence A116636 A116637 A116638
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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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