A135254 Binomial transform of A131666.

0, 0, 1, 4, 12, 33, 90, 252, 729, 2160, 6480, 19521, 58806, 176904, 531441, 1595052, 4785156, 14353281, 43053282, 129146724, 387420489, 1162241784, 3486725352, 10460235105, 31380882462, 94143001680, 282429536481, 847289140884

Offset: 0

Author

Paul Curtz, Nov 30 2007

Keywords

• nonn

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).

Crossrefs

Cf. A133474.

Programs

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

Magma

R:=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

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 *)

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

Sage

def A135254_list(prec):
    P. = 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

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)

Extensions

More terms from R. J. Mathar, Apr 02 2008