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A274324
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Number of partitions of n^3 into at most two parts.
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3
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1, 1, 5, 14, 33, 63, 109, 172, 257, 365, 501, 666, 865, 1099, 1373, 1688, 2049, 2457, 2917, 3430, 4001, 4631, 5325, 6084, 6913, 7813, 8789, 9842, 10977, 12195, 13501, 14896, 16385, 17969, 19653, 21438, 23329, 25327, 27437, 29660, 32001, 34461, 37045, 39754
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OFFSET
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0,3
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LINKS
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FORMULA
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Coefficient of x^(n^3) in 1/((1-x)*(1-x^2)).
a(n) = (3+(-1)^n+2*n^3)/4.
a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5) for n>4.
G.f.: (1-2*x+4*x^2+3*x^3) / ((1-x)^4*(1+x)).
E.g.f.: ((2 + x + 3*x^2 + x^3)*cosh(x) + (1 + x + 3*x^2 + x^3)*sinh(x))/2. (End)
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MAPLE
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MATHEMATICA
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PROG
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(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)).
b(n) = (3+(-1)^n+2*n)/4
vector(50, n, n--; b(n^3))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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