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

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

Crossrefs

Cf. A000023, A000045, A033811.

Sequence in context: A015224 A163983 A191829 * A074837 A286308 A015942

Adjacent sequences: A023617 A023618 A023619 * A023621 A023622 A023623

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 1998

Extensions

More terms from Colin Barker, May 14 2014

Status

approved