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

Author

Clark Kimberling, Jun 14 1998

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000023, A000045, A033811.

Programs

PARI

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

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

Extensions

More terms from Colin Barker, May 14 2014