A167682 Expansion of (1 - 2*x + 5*x^2) / (1 - 3*x)^2.

1, 4, 20, 84, 324, 1188, 4212, 14580, 49572, 166212, 551124, 1810836, 5904900, 19131876, 61647156, 197696052, 631351908, 2008846980, 6370914708, 20145865428, 63536960196, 199908972324, 627621192180, 1966546402164, 6150687683364, 19205208480708

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-9).

Formula

a(0)=1, a(1)=4, a(2)=20, a(n) = 6*a(n-1) - 9*a(n-2) for n>2.

a(n) = 4*A081038(n-1) for n>0.

a(n) = Sum_{k=0..n} A167666(n,k)*3^k.

a(n) = 3^(n - 2)*(8*n + 4) for n>0. - Colin Barker, Jan 21 2017

Mathematica

CoefficientList[Series[(1-2x+5*x^2)/(1-3x)^2, {x, 0, 40}], x] (* or *) Join[{1}, LinearRecurrence[{6, -9}, {4, 20}, 40]] (* Harvey P. Dale, Oct 20 2011 *)

Prog

(PARI) Vec((1-2*x+5*x^2) / (1-3*x)^2 + O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Sequence in context: A217482 A099898 A003489 * A246574 A155721 A084240

Adjacent sequences: A167679 A167680 A167681 * A167683 A167684 A167685

Keyword

nonn,easy

Author

Philippe Deléham, Nov 09 2009

Extensions

Corrected and extended by Harvey P. Dale, Oct 20 2011

PARI code corrected by Colin Barker, Jan 21 2017

Status

approved