A023553 Convolution of integers >= 3 and Lucas numbers.

3, 13, 29, 58, 106, 186, 317, 531, 879, 1444, 2360, 3844, 6247, 10137, 16433, 26622, 43110, 69790, 112961, 182815, 295843, 478728, 774644, 1253448, 2028171, 3281701, 5309957, 8591746

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A000204 (Lucas numbers).

Programs

Mathematica

Flatten[Table[ListConvolve[Range[3,n+2],LucasL[Range[n]]],{n,30}]] (* Harvey P. Dale, Sep 25 2015 *)

Formula

G.f.: (x*(3 + 4*x - 4*x^2))/((1 - x - x^2)*(1-x)^2). - Ralf Stephan, Apr 28 2004

a(n) = a(n-1) + a(n-2) + 3*n + 4. - Christian Krause, Dec 07 2023