A242496 a(n)=sum_{j=0..n} sum_{i=0..j} F(i)*L(j), where F(n)=A000045(n) and L(n)=A000032(n).

0, 1, 7, 23, 72, 204, 564, 1521, 4059, 10747, 28336, 74504, 195576, 512865, 1344063, 3521007, 9221688, 24148468, 63230860, 165555665, 433454835, 1134839091, 2971111392, 7778574288, 20364739632, 53315851969, 139583151799, 365434146311, 956720165544

Offset: 0

Author

J. M. Bergot, May 16 2014

Keywords

• nonn
• easy

Examples

			For n=5, 0*(2+1+3+4+7+11) + 1*(1+3+4+7+11) + 1*(3+4+7+11) + 2*(4+7+11) + 3*(7+11) + 5*11 = 204 = F(2*5+3) - L(n+2) + 0 = 233-29 = 204.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-2,-6,4,2,-1).

Crossrefs

Cf. A190173, A000045, A000032, A242300.

Programs

Maple

A242496 := proc(n)
    add(add(A000045(i)*A000032(j),i=0..j),j=0..n) ;
end proc: # R. J. Mathar, May 17 2014

Mathematica

LinearRecurrence[{4,-2,-6,4,2,-1},{0,1,7,23,72,204},30] (* Harvey P. Dale, Oct 03 2020 *)

PARI

F(n) = fibonacci(n)
L(n) = if(n==0, 2, F(2*n)/F(n))
vector(30, n, sum(i=0, n-1, sum(j=i, n-1, F(i)*L(j)))) \\ Colin Barker, May 16 2014

Formula

a(n) = A001519(n+2) - A000032(n+2) + A059841(n).

a(n) = L(n)*F(n+3) - L(n+2) + (1-3*(-1)^n)/2. - Colin Barker, May 18 2014

G.f.: -x*(3*x^2-3*x-1) / ((x-1)*(x+1)*(x^2-3*x+1)*(x^2+x-1)). - Colin Barker, May 16 2014

Extensions

Two terms corrected, and more terms added by Colin Barker, May 16 2014

Formula corrected by Colin Barker, May 17 2014