A268484 - OEIS

A268484

a(n) = (n + 1)*(4*n^2 + 14*n + 9)/3.

3, 18, 53, 116, 215, 358, 553, 808, 1131, 1530, 2013, 2588, 3263, 4046, 4945, 5968, 7123, 8418, 9861, 11460, 13223, 15158, 17273, 19576, 22075, 24778, 27693, 30828, 34191, 37790, 41633, 45728, 50083, 54706, 59605, 64788, 70263, 76038, 82121, 88520, 95243

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OFFSET

0,1

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.: (3 + 6*x - x^2)/(x - 1)^4.

a(n) = Sum_{k = 0..n} (2*k + 1)*(2*k + 3) = Sum_{k = 0..n} A005408(k)*A005408(k + 1).

Sum_{n>=0} 1/a(n) = 0.4315109123788144393864...

EXAMPLE

a(0) = 1*3 = 3;