A162746 Row sums of Fibonacci-Pascal triangle A162745.

1, 2, 5, 14, 42, 132, 427, 1402, 4629, 15290, 50412, 165816, 544253, 1783602, 5839313, 19106766, 62504002, 204457540, 668825279, 2188016442, 7158417217, 23421034442, 76632061852, 250740203864, 820430583305, 2684486330562, 8783760256301, 28740810537518, 94040879244602

Offset

0,2

Comments

Second binomial transform of aerated Fibonacci numbers.

Hankel transform is 1,1,1,-1,0,0,0,...

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (8,-23,28,-11).

Formula

G.f.: (1-2x)^3/(1-8x+23x^2-28x^3+11x^4);

a(n) = Sum_{k=0..floor(n/2)} C(n,2k)*2^(n-2k)*F(k+1).

a(n) = Sum_{k=0..n} C(n,k)*2^(n-k)*F(k/2+1)*(1+(-1)^k)/2.

Mathematica

LinearRecurrence[{8, -23, 28, -11}, {1, 2, 5, 14}, 30] (* Harvey P. Dale, Oct 05 2023 *)

Prog

(PARI) T(n, k) = sum(j=0, n, binomial(n, j)*binomial(n-j, 2*(k-j))*fibonacci(k-j+1));
a(n) = vecsum(vector(n+1, k, T(n, k-1))); \\ Michel Marcus, Nov 11 2022

Crossrefs

Cf. A162745.

Sequence in context: A287969 A061922 A293498 * A148329 A293499 A024175

Adjacent sequences: A162743 A162744 A162745 * A162747 A162748 A162749

Keyword

easy,nonn

Author

Paul Barry, Jul 12 2009

Status

approved