OFFSET
0,2
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).
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
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 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x+x^2)/(1-5*x-5*x^2)) \\ 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
(Sage)
def A123887_list(prec):
P.<x> = 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
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 20 2006
STATUS
approved