OFFSET
0,2
COMMENTS
a(n+1)/a(n) tends to A156035.
FORMULA
a(n) = 2*Sum_{k=1..n} Fibonacci(k)*(A008288(n-1,n-k) + A008288(n-1,n-k-1)). - Andrew Howroyd, May 29 2021
G.f.: x*(3*x^2-18*x+3-(x+1)*sqrt(x^2-6*x+1))/((x^2-7*x+1)*(x^2-6*x+1)). - Alois P. Heinz, May 29 2021
a(n) = ((79-97*n+26*n^2)*a(n-1) + (-9+9*n-2*n^2)*a(n-4) + (107-111*n+26*n^2)*a(n-3) + (-322+352*n-88*n^2)*a(n-2)) / (5-7*n+2*n^2) for n >= 4. - José María Grau Ribas, Jun 19 2021
MATHEMATICA
F[0, 0] = 0; F[m_, 0] := Fibonacci[m]; F[0, n_] := Fibonacci[n];
F[m_, n_] := F[m, n] = F[m - 1 , n ] + F[m , n - 1] + F[m - 1, n - 1];
Table[F[n, n], {n, 0, 100}]
PROG
(PARI) \\ here D(n, k) is A008288(n, k).
D(n, k) = {sum(d = 0, min(n, k), binomial(k, d)*binomial(n+k-d, k))}
a(n) = {2*sum(k=1, n, fibonacci(k)*(D(n-1, n-k) + D(n-1, n-k-1)))} \\ Andrew Howroyd, May 29 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
José María Grau Ribas, May 24 2021
STATUS
approved