A016191 Expansion of 1/((1-9x)*(1-12x)).

1, 21, 333, 4725, 63261, 818181, 10349613, 128978325, 1590786621, 19476859941, 237209103693, 2877890303925, 34817113183581, 420347224031301, 5067043480830573, 61010412902061525, 733977975013590141

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (21, -108).

Formula

a(n) = (12^(n+1) - 9^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005

a(n-1) = Sum_{k=1..n} 3^(n-1)*3^(n-k)*binomial(n, k). - Zerinvary Lajos, Sep 24 2006

a(n) = 12*a(n-1) + 9^n, a(0)=1. - Vincenzo Librandi, Feb 09 2011

a(n) = 21*a(n-1) - 108*a(n-2); a(0)=1, a(1)=21. - Vincenzo Librandi, Feb 09 2011

Mathematica

CoefficientList[Series[1/((1-9x)(1-12x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{21, -108}, {1, 21}, 30] (* Harvey P. Dale, Oct 15 2011 *)

Prog

(PARI) Vec(1/((1-9*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Sequence in context: A091947 A016195 A322540 * A297336 A095905 A051525

Adjacent sequences: A016188 A016189 A016190 * A016192 A016193 A016194

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved