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

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Cf. A000045, A033192.

Programs

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}] (* or *) LinearRecurrence[ {4,-2,-6,4,2,-1},{1,2,2,4,7,16},30] (* Harvey P. Dale, Feb 02 2015 *)

Formula

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

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