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A160805
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a(n) = (2*n^3 + 9*n^2 + n + 24) / 6.
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3
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4, 6, 13, 27, 50, 84, 131, 193, 272, 370, 489, 631, 798, 992, 1215, 1469, 1756, 2078, 2437, 2835, 3274, 3756, 4283, 4857, 5480, 6154, 6881, 7663, 8502, 9400, 10359, 11381, 12468, 13622, 14845, 16139, 17506, 18948, 20467, 22065, 23744, 25506, 27353, 29287
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OFFSET
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0,1
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COMMENTS
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Arithmetic progression of third order; a(n+1)-a(n) = A008865(n+2);
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REFERENCES
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R. Courant, Differential and Integral Calculus Vol. I (Blackie&Son, 1937), ch. I.4, Example 5, p.29.
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LINKS
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FORMULA
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a(n) = (2*n^3 + 9*n^2 + n + 24) / 6.
G.f.: (4-10*x+13*x^2-5*x^3)/(x-1)^4.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4), n>3. (End)
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MAPLE
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MATHEMATICA
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Table[(2 n^3 + 9 n^2 + n + 24)/6, {n, 0, 60}]
CoefficientList[Series[(4 - 10*x + 13*x^2 - 5*x^3)/(x - 1)^4, {x, 0, 60}], x] (* Wesley Ivan Hurt, Aug 29 2015 *)
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PROG
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(PARI) first(m)=vector(m, i, i--; (2*i^3 + 9*i^2 + i + 24) / 6) \\ Anders Hellström, Aug 29 2015
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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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