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A133474 Inverse binomial transform of (A113405 preceded by 0). 3
0, 0, 0, 1, 6, 24, 81, 252, 756, 2241, 6642, 19764, 59049, 176904, 530712, 1592865, 4780782, 14346720, 43046721, 129146724, 387440172, 1162300833, 3486843450, 10460412252, 31381059609, 94143001680, 282429005040, 847287546561 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

b(n) = a(n) with one 0; c(n)=1, 3, 6, 9, 9, 0, -27, ... = A057083; b(n+1) = 3*b(n) + c(n)?

From R. J. Mathar, Apr 02 2008: (Start)

O.g.f.: x^3/((1-3*x)*(1-3*x+3*x^2)).

a(n) = 6*a(n-1) - 12*a(n-2) + 9*a(n-3). (End)

MAPLE

seq(coeff(series(x^3/((1-3*x)(1-3*x+3*x^2)), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Nov 21 2019

MATHEMATICA

LinearRecurrence[{6, -12, 9}, {0, 0, 0, 1}, 30] (* G. C. Greubel, Nov 21 2019 *)

PROG

(PARI) my(x='x+O('x^30)); concat([0, 0, 0], Vec(x^3/((1-3*x)*(1-3*x+3*x^2)))) \\ G. C. Greubel, Nov 21 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); [0, 0, 0] cat Coefficients(R!( x^3/((1-3*x)*(1-3*x+3*x^2)) )); // G. C. Greubel, Nov 21 2019

(Sage)

def A133474_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P(x^3/((1-3*x)*(1-3*x+3*x^2))).list()

A133474_list(30) # G. C. Greubel, Nov 21 2019

(GAP) a:=[0, 0, 1];; for n in [4..30] do a[n]:=6*a[n-1]-12*a[n-2]+9*a[n-3]; od; a; # G. C. Greubel, Nov 21 2019

CROSSREFS

Cf. A047790, A131571.

Sequence in context: A068711 A320856 A047790 * A052150 A118043 A317408

Adjacent sequences:  A133471 A133472 A133473 * A133475 A133476 A133477

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Nov 29 2007

STATUS

approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)