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A023620

Convolution of Lucas numbers and odd numbers.

1, 6, 18, 41, 82, 152, 269, 462, 778, 1293, 2130, 3488, 5689, 9254, 15026, 24369, 39490, 63960, 103557, 167630, 271306, 439061, 710498, 1149696, 1860337, 3010182, 4870674, 7881017, 12751858, 20633048, 33385085, 54018318, 87403594, 141422109, 228825906

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..35.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

FORMULA

a(n) = L(5)*(F(n+1)-1) + L(4)*F(n) - L(3)*n - 2*n, F(n) = A000045(n).

a(n) = A033811(n) - 2n. - N. J. A. Sloane, Jun 12 2004

a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). G.f.: -x*(x+1)*(2*x+1) / ((x-1)^2*(x^2+x-1)). - Colin Barker, May 14 2014

PROG

(PARI) Vec(-x*(x+1)*(2*x+1)/((x-1)^2*(x^2+x-1)) + O(x^100)) \\ Colin Barker, May 14 2014