A099504 Expansion of 1/(1-5*x+x^3).

1, 5, 25, 124, 615, 3050, 15126, 75015, 372025, 1844999, 9149980, 45377875, 225044376, 1116071900, 5534981625, 27449863749, 136133246845, 675131252600, 3348206399251, 16604898749410, 82349362494450, 408398606072999

Offset

0,2

Comments

A transform of A000351 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3)).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 5*a(n-1) - a(n-3).

a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k, k)*(-1)^k*5^(n-3*k).

Maple

A099504:=n->sum(binomial(n-2*i, i)*(-1)^i*5^(n-3*i), i=0..floor(n/3)); seq(A099504(n), n=0..30); # Wesley Ivan Hurt, Dec 03 2013

Mathematica

Table[Sum[Binomial[n-2*i, i]*(-1)^i*5^(n-3*i), {i, 0, Floor[n/3]}], {n, 0, 30}] (* Wesley Ivan Hurt, Dec 03 2013 *)
LinearRecurrence[{5, 0, -1}, {1, 5, 25}, 30] (* G. C. Greubel, Aug 03 2023 *)

Prog

(Magma) [n le 3 select 5^(n-1) else 5*Self(n-1) -Self(n-3): n in [1..30]]; // G. C. Greubel, Aug 03 2023
(SageMath)
@CachedFunction
def a(n): # a = A099504
    if (n<3): return 5^n
    else: return 5*a(n-1) - a(n-3)
[a(n) for n in range(31)] # G. C. Greubel, Aug 03 2023

Crossrefs

Cf. A000071, A000351, A076264, A099503.

Sequence in context: A086093 A171279 A231636 * A299958 A036156 A097756

Adjacent sequences: A099501 A099502 A099503 * A099505 A099506 A099507

Keyword

easy,nonn

Author

Paul Barry, Oct 20 2004

Status

approved