A032441 a(n) = Sum_{i=0..2} binomial(Fibonacci(n),i).

1, 2, 2, 4, 7, 16, 37, 92, 232, 596, 1541, 4006, 10441, 27262, 71254, 186356, 487579, 1276004, 3339821, 8742472, 22885996, 59912932, 156848617, 410626154, 1075018897, 2814412826, 7368190922, 19290113572, 50502074767, 132215989336, 346145696821, 906220783316

Offset

0,2

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (4,-2,-6,4,2,-1).

Formula

a(n) = 4*a(n-1) - 2*a(n-2) - 6*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6); a(0)=1, a(1)=a(2)=2, a(3)=4, a(4)=7, a(5)=16. - Harvey P. Dale, Feb 02 2015

a(n) = A033192(n) + 1. - Alois P. Heinz, Jul 01 2018

G.f.: (1-2*x-4*x^2+6*x^3+3*x^4-2*x^5) / ((-1+x) * (1+x) * (1-3*x+x^2) * (-1+x+x^2)). - Elmo R. Oliveira, May 06 2026

Maple

a:= n-> (f-> f*(f+1)/2+1)((<<0|1>, <1|1>>^n)[1, 2]):
seq(a(n), n=0..35);  # Alois P. Heinz, Jul 01 2018

Mathematica

Table[Sum[Binomial[Fibonacci[n], i], {i, 0, 2}], {n, 0, 30}] (* Harvey P. Dale, Feb 02 2015 *)
(* Alternative: *)
LinearRecurrence[ {4, -2, -6, 4, 2, -1}, {1, 2, 2, 4, 7, 16}, 30] (* Harvey P. Dale, Feb 02 2015 *)

Crossrefs

Cf. A000045, A033192.

Sequence in context: A052949 A014266 A380360 * A238184 A340333 A065844

Adjacent sequences: A032438 A032439 A032440 * A032442 A032443 A032444

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved