OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-12,9).
FORMULA
From R. J. Mathar, Apr 02 2008: (Start)
O.g.f.: x^2*(1-2*x)/((1 - 3*x + 3*x^2)*(1-3*x)).
a(n) = 6*a(n-1) - 12*a(n-2) + 9*a(n-3). (End)
MAPLE
seq(coeff(series(x^2*(1-2*x)/((1-3*x+3*x^2)*(1-3*x)), x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 21 2019
MATHEMATICA
CoefficientList[Series[x^2(2x-1)/((3x^2-3x+1)(3x-1)), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -12, 9}, {0, 0, 1, 4}, 30] (* Harvey P. Dale, May 26 2011 *)
PROG
(PARI) my(x='x+O('x^30)); concat([0, 0], Vec(x^2*(1-2*x)/((1-3*x+3*x^2)*(1-3*x)))) \\ G. C. Greubel, Nov 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0, 0] cat Coefficients(R!( x^2*(1-2*x)/((1-3*x+3*x^2)*(1-3*x)) )); // G. C. Greubel, Nov 21 2019
(Sage)
def A135254_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x^2*(1-2*x)/((1-3*x+3*x^2)*(1-3*x))).list()
A135254_list(30) # G. C. Greubel, Nov 21 2019
(GAP) a:=[0, 1, 4];; for n in [4..30] do a[n]:=6*a[n-1]-12*a[n-2]+9*a[n-3]; od; Concatenation([0], a); # G. C. Greubel, Nov 21 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, Nov 30 2007
EXTENSIONS
More terms from R. J. Mathar, Apr 02 2008
STATUS
approved