A133474 Inverse binomial transform of (A113405 preceded by 0).

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

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: A344273 A320856 A047790 * A052150 A118043 A317408

Adjacent sequences: A133471 A133472 A133473 * A133475 A133476 A133477

Keyword

nonn,easy

Author

Paul Curtz, Nov 29 2007

Status

approved