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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
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OFFSET
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0,3
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COMMENTS
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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] * ... - Mats Granvik, Gary W. Adamson, Aug 07 2009
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LINKS
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FORMULA
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G.f.: Product_{j>=1} (1 + x^j + x^(2j) + x^(4j)/(1-x^j)).
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EXAMPLE
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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
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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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MATHEMATICA
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nmax = 50; CoefficientList[Series[Product[(1 - x^(3*k) + x^(4*k))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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