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A135254 Binomial transform of A131666. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A133474.

Sequence in context: A027941 A293064 A219092 * A326804 A000754 A317974

Adjacent sequences:  A135251 A135252 A135253 * A135255 A135256 A135257

KEYWORD

nonn

AUTHOR

Paul Curtz, Nov 30 2007

EXTENSIONS

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

STATUS

approved

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)