A123871 Expansion of g.f.: (1+x+x^2)/(1-4*x-4*x^2).

1, 5, 25, 120, 580, 2800, 13520, 65280, 315200, 1521920, 7348480, 35481600, 171320320, 827207680, 3994112000, 19285278720, 93117562880, 449611366400, 2170915717120, 10482108334080, 50612096204800, 244376818155520, 1179955657441280, 5697329902387200

Offset: 0

Author

N. J. A. Sloane, Nov 20 2006

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• A. Burstein and T. Mansour, Words restricted by 3-letter ..., Annals of Combinatorics 7 (2003), 1-14. arXiv:math.CO/0112281
• Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
• Index entries for linear recurrences with constant coefficients, signature (4,4).

Crossrefs

Column 5 in A265584.

Programs

GAP

a:=[1,5,25];; for n in [4..30] do a[n]:=4*a[n-1]+4*a[n-2]; od; a; # G. C. Greubel, Aug 08 2019

Magma

I:=[1, 5, 25]; [n le 3 select I[n] else 4*Self(n-1)+4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 27 2012

Maple

seq(coeff(series((1+x+x^2)/(1-4*x-4*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Aug 08 2019

Mathematica

CoefficientList[Series[(1+x+x^2)/(1-4*x-4*x^2),{x,0,30}],x] (* Vincenzo Librandi, Jun 27 2012 *)
LinearRecurrence[{4,4},{1,5,25},30] (* Harvey P. Dale, Mar 25 2022 *)

PARI

my(x='x+O('x^30)); Vec((1+x+x^2)/(1-4*x-4*x^2)) \\ G. C. Greubel, Aug 08 2019

Sage

def A123871_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x+x^2)/(1-4*x-4*x^2) ).list()
A123871_list(30) # G. C. Greubel, Aug 08 2019

Formula

a(n) = 4*a(n-1) + 4*a(n-2) for n>2. - Philippe Deléham, Sep 19 2009