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A332698
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a(n) = (8*n^3 + 15*n^2 + 13*n)/6.
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1
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0, 6, 25, 65, 134, 240, 391, 595, 860, 1194, 1605, 2101, 2690, 3380, 4179, 5095, 6136, 7310, 8625, 10089, 11710, 13496, 15455, 17595, 19924, 22450, 25181, 28125, 31290, 34684, 38315, 42191, 46320, 50710, 55369, 60305, 65526, 71040, 76855, 82979, 89420, 96186
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OFFSET
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0,2
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COMMENTS
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The end values of the partial rows on the main diagonal of A332662 in the representation in the example section.
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LINKS
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FORMULA
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a(n) = [x^n] (x*(x^2 + x + 6))/(x - 1)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = binomial(n+2, 3) + binomial(n+1, 3) + 2*(n+1)*binomial(n+1, 2) + binomial(n, 1) = A331987(n) + n.
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MAPLE
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a := n -> (8*n^3 + 15*n^2 + 13*n)/6: seq(a(n), n=0..41);
gf := (x*(x^2 + x + 6))/(x - 1)^4: ser := series(gf, x, 44):
seq(coeff(ser, x, n), n=0..41);
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {0, 6, 25, 65}, 42]
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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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