A303609 - OEIS

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A303609

a(n) = 2*n^3 + 9*n^2 + 9*n.

0, 20, 70, 162, 308, 520, 810, 1190, 1672, 2268, 2990, 3850, 4860, 6032, 7378, 8910, 10640, 12580, 14742, 17138, 19780, 22680, 25850, 29302, 33048, 37100, 41470, 46170, 51212, 56608, 62370, 68510, 75040, 81972, 89318, 97090, 105300, 113960, 123082, 132678, 142760

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OFFSET

0,2

COMMENTS

y-values solving the Diophantine equation 4*x^3 + 9*x^2 = y^2 for positive x (which are listed in A028552). The equation is also satisfied by y=2 and x=-2.

LINKS

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: 2*x*(10 - 5*x + x^2) / (1 - x)^4.

a(n) = n*(2*n^2 + 9*n + 9) = n * A014107(n+3).

MATHEMATICA

Table[2 n^3 + 9 n^2 + 9 n, {n, 0, 40}] (* or *) CoefficientList[Series[(20 x - 10 x^2 + 2 x^3) / (1 - x)^4, {x, 0, 33}], x]

PROG

(Magma) [2*n^3+9*n^2+9*n: n in [0..40]]

(GAP) List([0..50], n->n*(2*n^2+9*n+9)); # Muniru A Asiru, Apr 29 2018

CROSSREFS