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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).
2
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
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
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