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A118807
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Number of partitions of n having no parts with multiplicity 3.
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11
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1, 1, 2, 2, 5, 6, 9, 12, 19, 24, 34, 43, 62, 77, 105, 132, 177, 220, 287, 356, 462, 570, 723, 888, 1121, 1370, 1705, 2074, 2570, 3111, 3816, 4601, 5617, 6743, 8170, 9777, 11794, 14058, 16858, 20029, 23932, 28334, 33692, 39772, 47133, 55468, 65471, 76840
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Column 0 of A118806.
Infinite convolution product of [1,1,1,0,1,1,1,1,1,1] aerated n-1 times. i.e. [1,1,1,0,1,1,1,1,1,1] * [1,0,1,0,1,0,0,0,1,0] * [1,0,0,1,0,0,1,0,0,0] * ... [From Mats Granvik, Gary W. Adamson, Aug 07 2009]
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..1000
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FORMULA
| G.f.: product(1+x^j+x^(2j)+x^(4j)/(1-x^j), j=1..infinity).
a(n) = A000041(n)-A183560(n) = A183568(n,0)-A183568(n,3). - Alois P. Heinz, Oct 09 2011
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EXAMPLE
| a(6) = 9 because among the 11 (=A000041(6)) partitions of 6 only [2,2,2] and [3,1,1,1] have parts with multiplicity 3.
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MAPLE
| g:=product(1+x^j+x^(2*j)+x^(4*j)/(1-x^j), j=1..60): gser:=series(g, x=0, 55): seq(coeff(gser, x, n), n=0..50);
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CROSSREFS
| Cf. A000041, A118806, A007690, A116645, A183560, A183568.
Sequence in context: A054255 A063177 A034803 * A098507 A097066 A035548
Adjacent sequences: A118804 A118805 A118806 * A118808 A118809 A118810
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2006
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