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A016191 Expansion of 1/((1-9x)*(1-12x)). 2
1, 21, 333, 4725, 63261, 818181, 10349613, 128978325, 1590786621, 19476859941, 237209103693, 2877890303925, 34817113183581, 420347224031301, 5067043480830573, 61010412902061525, 733977975013590141 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 18 17:45 EST 2019. Contains 329287 sequences. (Running on oeis4.)