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

0,2

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).

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.

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 *)

Prog

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

Crossrefs

Cf. A060926, A060927.

Sequence in context: A082308 A270767 A026718 * A002002 A182626 A351050

Adjacent sequences: A060925 A060926 A060927 * A060929 A060930 A060931

Keyword

nonn,easy

Author

Wolfdieter Lang, Apr 20 2001

Status

approved