A067332 Convolution of Fibonacci F(n+1), n>=0, with F(n+4), n>=0.

3, 8, 19, 40, 80, 154, 289, 532, 965, 1730, 3072, 5412, 9471, 16480, 28535, 49196, 84496, 144638, 246845, 420140, 713353, 1208518, 2043264, 3448200, 5809275, 9771704, 16413019, 27530992, 46122320

Offset: 0

Author

Wolfdieter Lang, Feb 15 2002

Keywords

• nonn
• easy

Comments

Fourth diagonal of A067330. Fourth column of A067418.

Links

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

Programs

Mathematica

Table[((11n+15)Fibonacci[n+1]+7(n+1)Fibonacci[n])/5,{n,0,30}] (* or *) LinearRecurrence[{2,1,-2,-1},{3,8,19,40},30] (* Harvey P. Dale, Aug 25 2014 *)

Formula

a(n)= A067330(n+3, n) = A067418(n+3, 3) = sum(F(k+1)*F(n+4-k), k=0..n), n>=0.

a(n)= ((11*n+15)*F(n+1)+7*(n+1)*F(n))/5, with F(n) := A000045(n) (Fibonacci).

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

a(0)=3, a(1)=8, a(2)=19, a(3)=40, a(n)=2*a(n-1)+a(n-2)-2*a(n-3)-a(n-4). - Harvey P. Dale, Aug 25 2014