A060928 Expansion of 1/(1 - 5*x - 4*x^3).

1, 5, 25, 129, 665, 3425, 17641, 90865, 468025, 2410689, 12416905, 63956625, 329425881, 1696797025, 8739811625, 45016761649, 231870996345, 1194314228225, 6151638187721, 31685674923985, 163205631532825

Offset: 0

Author

Wolfdieter Lang, Apr 20 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (5,0,4).

Crossrefs

Cf. A060926, A060927.

Programs

Magma

I:=[1, 5, 25, 129]; [n le 3 select I[n] else 5*Self(n-1) + 4*Self(n-3): n in [1..31]]; // G. C. Greubel, Apr 07 2021

Maple

m:= 40; S:= series( 1/(1-5*x-4*x^3), x, m+1);
seq(coeff(S, x, j), j = 0..m); # G. C. Greubel, Apr 07 2021

Mathematica

CoefficientList[Series[1/(1-5x-4x^3),{x,0,30}],x] (* or *) LinearRecurrence[ {5,0,4}, {1,5,25}, 30] (* Harvey P. Dale, Apr 09 2018 *)

PARI

{ for (n=0, 30, if (n>2, a=5*a1 + 4*a3; a3=a2; a2=a1; a1=a, if (n==0, a=a3=1, if (n==1, a=a2=5, a=a1=25))); print1(a, ", "); ) } \\ Harry J. Smith, Jul 14 2009

Sage

def A060928_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( 1/(1-5*x-4*x^3) ).list()
A060928_list(30) # G. C. Greubel, Apr 07 2021

Formula

G.f.: 1/(1 - 5*x - 4*x^3).

a(n) = 5*a(n-1) + 4*a(n-3), n >= 3, a(n) = 5^n, n = 0, 1, 2.