A016136 Expansion of 1/((1-2*x)*(1-12*x)).

1, 14, 172, 2072, 24880, 298592, 3583168, 42998144, 515977984, 6191736320, 74300836864, 891610044416, 10699320537088, 128391846453248, 1540702157455360, 18488425889497088, 221861110674030592, 2662333328088498176, 31947999937062240256, 383375999244747407360, 4600511990936969936896

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			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]
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (14,-24).

Programs

Magma

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

Magma

[&+[2^(n+i)*3^i: i in [0..n]]: n in [0..20]]; // 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 *)

PARI

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

Sage

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

Formula

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

From Vincenzo Librandi, Oct 09 2011: (Start)

a(n) = 2^n*(6^(n+1) - 1)/5.

a(n) = 14*a(n-1) - 24*a(n-2). (End)

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

E.g.f.: exp(2*x)*(exp(10*x) - 1)/10. - Elmo R. Oliveira, Mar 08 2025