A032439 a(n) = Sum_{i=0..4} binomial(Fibonacci(n),i).

1, 2, 2, 4, 8, 31, 163, 1093, 7547, 52956, 368831, 2559196, 17676661, 121774888, 837294004, 5750356236, 39462206694, 270686172409, 1856193470231, 12726292640107, 87243213304941, 598041351085972

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1198

Index entries for linear recurrences with constant coefficients, signature (11,-17,-124,276,396,-902,-462,946,220,-340,-44,39,3,-1).

Formula

G.f.: ( 1- 9*x -3*x^2 +140*x^3 -30*x^4 -689*x^5 +12*x^6 +1189*x^7 +129*x^8 -572*x^9 -46*x^10 +77*x^11 +5*x^12 -2*x^13 ) / ( (x-1) *(1+x) *(x^2+4*x-1) *(x^2-7*x+1) *(x^2+3*x+1) *(x^2-x-1) *(x^2-3*x+1) *(x^2+x-1) ). - Robert Israel, Mar 06 2019

Maple

ff:= unapply(expand(add(binomial(x, i), i=0..4)), x):
seq(ff(combinat:-fibonacci(n)), n=0..50); # Robert Israel, Mar 06 2019

Mathematica

LinearRecurrence[{11, -17, -124, 276, 396, -902, -462, 946, 220, -340, -44, 39, 3, -1}, {1, 2, 2, 4, 8, 31, 163, 1093, 7547, 52956, 368831, 2559196, 17676661, 121774888}, 50] (* Georg Fischer May 09 2020 *)

Prog

(PARI) a(n) = my(fn=fibonacci(n)); sum(i=0, 4, binomial(fn, i)); \\ Michel Marcus, May 09 2020

Crossrefs

Sequence in context: A325514 A032440 A145869 * A096096 A300759 A100799

Adjacent sequences: A032436 A032437 A032438 * A032440 A032441 A032442

Keyword

nonn

Author

N. J. A. Sloane

Status

approved