A123887 Expansion of g.f.: (1+x+x^2)/(1-5*x-5*x^2).

1, 6, 36, 210, 1230, 7200, 42150, 246750, 1444500, 8456250, 49503750, 289800000, 1696518750, 9931593750, 58140562500, 340360781250, 1992506718750, 11664337500000, 68284221093750, 399742792968750, 2340135070312500, 13699389316406250, 80197621933593750, 469485056250000000

Offset: 0

Author

N. J. A. Sloane, Nov 20 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• A. Burstein and T. Mansour, Words restricted by 3-letter ..., arXiv:math/0112281 [math.CO], 2001.
• A. Burstein and T. Mansour, Words Restricted by 3-Letter Generalized Multipermutation Patterns, Annals. Combin., 7 (2003), 1-14.
• 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 (5,5).

Crossrefs

Column 6 in A265584.

Programs

GAP

a:=[6,36];; for n in [3..30] do a[n]:=5*(a[n-1]+a[n-2]); od; Concatenation([1], a); # G. C. Greubel, Aug 07 2019

Magma

I:=[6,36]; [1] cat [n le 2 select I[n] else 5*(Self(n-1)+ Self(n-2)): n in [1..30]]; // G. C. Greubel, Aug 07 2019

Maple

seq(coeff(series((1+x+x^2)/(1-5*x-5*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Aug 07 2019

Mathematica

CoefficientList[Series[(1+x+x^2)/(1-5x-5x^2),{x,0,30}],x] (* or *) LinearRecurrence[{5,5},{1,6,36}, 40] (* Harvey P. Dale, Jan 03 2019 *)

PARI

my(x='x+O('x^30)); Vec((1+x+x^2)/(1-5*x-5*x^2)) \\ G. C. Greubel, Aug 07 2019

Sage

def A123887_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x+x^2)/(1-5*x-5*x^2) ).list()
A123887_list(30) # G. C. Greubel, Aug 07 2019

Formula

a(0)=1, a(1)=6, a(2)=36, a(n) = 5*a(n-1) + 5*a(n-2) for n>2. - Philippe Deléham, Sep 19 2009