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A162746
Row sums of Fibonacci-Pascal triangle A162745.
1
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,...
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 12 2009
STATUS
approved