A032440 Sum_{i=0..3} binomial(Fibonacci(n),i).

1, 2, 2, 4, 8, 26, 93, 378, 1562, 6580, 27776, 117570, 497785, 2108418, 8930754, 37830676, 160251624, 678835194, 2875587605, 12181180442, 51600296826, 218582354212, 925929680832, 3922301042114, 16615133763313

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (5,0,-16,8,8,-3,-1).

Formula

G.f.: ( 1-3*x-8*x^2+10*x^3+12*x^4-6*x^5-2*x^6 ) / ( (x-1) *(x^2+4*x-1) *(x^2+x-1) *(x^2-x-1) ). - R. J. Mathar, May 08 2020

Maple

A032440 := proc(n)
    add(binomial(combinat[fibonacci](n), i), i=0..3)
end proc:
seq(A032440(n), n=0..40) ; # R. J. Mathar, May 08 2020

Crossrefs

Sequence in context: A064451 A223027 A325514 * A145869 A032439 A096096

Adjacent sequences: A032437 A032438 A032439 * A032441 A032442 A032443

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved