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A318765
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a(n) = (n + 2)*(n^2 + n - 1).
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1
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-2, 3, 20, 55, 114, 203, 328, 495, 710, 979, 1308, 1703, 2170, 2715, 3344, 4063, 4878, 5795, 6820, 7959, 9218, 10603, 12120, 13775, 15574, 17523, 19628, 21895, 24330, 26939, 29728, 32703, 35870, 39235, 42804, 46583, 50578, 54795, 59240, 63919, 68838, 74003, 79420, 85095
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OFFSET
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0,1
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COMMENTS
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a(n) is divisible by 11 for n = 3, 7, 9, 14, 18, 20, 25, 29, 31, 36, 40, ... with formula (1/3)*(11*m + (1 + (m mod 3))*(-1)^((m-1) mod 3) + 8), m >= 0.
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LINKS
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FORMULA
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O.g.f.: (-2 + 11*x - 4*x^2 + x^3)/(1 - x)^4.
E.g.f.: (-2 + 5*x + 6*x^2 + x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 5. - Wesley Ivan Hurt, Dec 18 2020
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MAPLE
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MATHEMATICA
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Table[(n + 2) (n^2 + n - 1), {n, 0, 50}]
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PROG
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(PARI) vector(50, n, n--; (n+2)*(n^2+n-1))
(Sage) [(n+2)*(n^2+n-1) for n in (0..50)]
(Maxima) makelist((n+2)*(n^2+n-1), n, 0, 50);
(GAP) List([0..50], n -> (n+2)*(n^2+n-1));
(Magma) [(n+2)*(n^2+n-1): n in [0..50]];
(Python) [(n+2)*(n**2+n-1) for n in range(50)]
(Julia) [(n+2)*(n^2+n-1) for n in 0:50] |> println
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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