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

0,3

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).

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A190173, A000045, A000032, A242300.

Sequence in context: A147972 A002223 A034563 * A356684 A048539 A240526

Adjacent sequences: A242493 A242494 A242495 * A242497 A242498 A242499

Keyword

nonn,easy

Author

J. M. Bergot, 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

Status

approved