OFFSET
0,2
COMMENTS
The numerator in Formula (3) in the JIS article should be 1-b*x, not 1-x.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..950
M. Katz, C. Stenson, Tiling a (2 x n)-board with squares and dominoes, JIS 12 (2009) 09.2.2, Table 1, a=2, b=3.
Index entries for linear recurrences with constant coefficients, signature (10,12,-27).
FORMULA
G.f.: ( 1-3*x ) / ( 1 - 10*x - 12*x^2 + 27*x^3 ).
MAPLE
seq(coeff(series((1-3*x)/(1-10*x-12*x^2+27*x^3), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 28 2019
MATHEMATICA
CoefficientList[Series[(1-3x)/(1-10x-12x^2+27x^3), {x, 0, 20}], x] (* Michael De Vlieger, Sep 30 2015 *)
LinearRecurrence[{10, 12, -27}, {1, 7, 82}, 30] (* Harvey P. Dale, Dec 30 2015 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1-3*x)/(1-10*x-12*x^2+27*x^3)) \\ G. C. Greubel, Oct 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-3*x)/(1-10*x-12*x^2+27*x^3) )); // G. C. Greubel, Oct 28 2019
(Sage)
def A253265_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-3*x)/(1-10*x-12*x^2+27*x^3)).list()
A253265_list(30) # G. C. Greubel, Oct 28 2019
(GAP) a:=[1, 7, 82];; for n in [4..30] do a[n]:=10*a[n-1]+12*a[n-2] -27*a[n-3]; od; a; # G. C. Greubel, Oct 28 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Sep 30 2015
STATUS
approved