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A016136 Expansion of 1/((1-2*x)*(1-12*x)). 1
1, 14, 172, 2072, 24880, 298592, 3583168, 42998144, 515977984, 6191736320, 74300836864, 891610044416, 10699320537088, 128391846453248, 1540702157455360, 18488425889497088, 221861110674030592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (14,-24).

FORMULA

a(n) = (12^n - 2^n)/10 for n>0. [Zerinvary Lajos, Jun 05 2009]

a(n) = 2^n*(6^(n+1)-1)/5 = 14*a(n-1)-24*a(n-2). - Vincenzo Librandi, Oct 09 2011

a(n) = Sum_{i=0..n} 2^(n+i)*3^i. [Bruno Berselli, Aug 28 2013]

EXAMPLE

For n=6, a(6) = 2^6+2^7*3+2^8*3^2+2^9*3^3+2^10*3^4+2^11*3^5+2^12*3^6 = 3583168. [Bruno Berselli, Aug 28 2013]

MATHEMATICA

CoefficientList[Series[1/((1 - 2*x)*(1 - 12*x)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Apr 08 2017 *)

PROG

(Sage) [(12^n - 2^n)/10 for n in xrange(1, 18)] /* Zerinvary Lajos, Jun 05 2009 */

(MAGMA) [2^n*(6^(n+1)-1)/5: n in [0..20]]; // Vincenzo Librandi, Oct 09 2011

(PARI) Vec(1/((1-2*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

(MAGMA) [&+[2^(n+i)*3^i: i in [0..n]]: n in [0..20]]; // Bruno Berselli, Aug 28 2013

CROSSREFS

Sequence in context: A014882 A048443 A191690 * A277940 A061484 A097583

Adjacent sequences:  A016133 A016134 A016135 * A016137 A016138 A016139

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 16 20:35 EDT 2019. Contains 328103 sequences. (Running on oeis4.)