A087425 a(n) = S(5*n,5)/S(n,5) where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).

23105, 459119455, 9758296035305, 208416652653910655, 4452963734477926435505, 95143212432467064852443605, 2032859482921447476046969568705, 43434715031065603778576465510557055

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Formula

a(n) = 121^n+{(21367+9555*sqrt(5))/2}^n+{(21367-9555*sqrt(5))/2}^n+{(1617+715*sqrt(5))/2}^n+{(1617-715*sqrt(5))/2}^n.

a(n) = (x_1)^n+(x_2)^n+(x_3)^n+(x_4)^n+(x_5)^n where (x_i) (1<=i<=5) are the roots of X^5-23105*X^4+37360785*X^3-4520654985*X^2+40931916905*X-25937424601.

Maple

S:=proc(n, m) add(binomial(n, k)*combinat:-fibonacci(m*k), k=0..n) end: m:=5: seq(S(m*n, m)/S(n, m), n=1..16); # Georg Fischer, Jul 07 2021

Crossrefs

Cf. A020876.

Cf. A087423 (m=3), A087424 (m=4).

Sequence in context: A104077 A199811 A230791 * A031648 A075784 A126301

Adjacent sequences: A087422 A087423 A087424 * A087426 A087427 A087428

Keyword

nonn

Author

Benoit Cloitre, Oct 22 2003

Status

approved