A101891 a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k)*Fibonacci(k+1).

1, 1, 2, 4, 9, 21, 49, 113, 258, 586, 1329, 3015, 6845, 15549, 35330, 80280, 182413, 414461, 941669, 2139477, 4860898, 11044006, 25092157, 57009871, 129527609, 294289401, 668631458, 1519143916, 3451524785, 7841931877, 17817022873

Offset

0,3

Comments

Transform of F(n+1) under the mapping g(x)-> (1/(1-x))g(x^2/((1-x)^2). Binomial transform of 1,0,1,0,2,0,3,0,5,...

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2,1)

Formula

G.f.: (1-x)^3/(1-4*x+5*x^2-2*x^3-x^4).

a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3)+a(n-4).

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

Crossrefs

Cf. A000045.

Sequence in context: A051164 A182904 A281425 * A119967 A266232 A052921

Adjacent sequences: A101888 A101889 A101890 * A101892 A101893 A101894

Keyword

easy,nonn

Author

Paul Barry, Dec 20 2004

Status

approved