A033813 Convolution of natural numbers n >= 1 with Lucas numbers L(k) (A000032) for k >= 3.

4, 15, 37, 77, 146, 262, 454, 769, 1283, 2119, 3476, 5676, 9240, 15011, 24353, 39473, 63942, 103538, 167610, 271285, 439039, 710475, 1149672, 1860312, 3010156, 4870647, 7880989, 12751829, 20633018, 33385054, 54018286, 87403561, 141422075, 228825871, 370248188

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn
• changed

Links

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

Crossrefs

Cf. A000032, A000045, A023548, A023553.

Programs

Mathematica

LinearRecurrence[{3,-2,-1,1},{4,15,37,77},40] (* or *) Rest[ CoefficientList[ Series[x (4+3x)/((1-x-x^2)(1-x)^2),{x,0,40}],x]] (* Harvey P. Dale, May 23 2011 *)

Formula

a(n) = L(6)*(F(n+1)-1)+L(5)*F(n)-L(4)*n, F(n): Fibonacci (A000045).

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

a(0)=4, a(1)=15, a(2)=37, a(3)=77, a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). - Harvey P. Dale, May 23 2011

Extensions

More terms from Jason Yuen, Aug 27 2025