A016159 Expansion of 1/((1-4*x)*(1-12*x)).

1, 16, 208, 2560, 30976, 372736, 4476928, 53739520, 644939776, 7739539456, 92875522048, 1114510458880, 13374142283776, 160489774514176, 1925877562605568, 23110531825008640, 277326386195070976, 3327916651520720896, 39934999886968127488, 479219998918495436800, 5750639988121456869376, 69007679861855528943616

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..920
• Index entries for linear recurrences with constant coefficients, signature (16,-48).

Programs

Magma

[2^(2*n-1)*(3^(n+1)-1): n in [0..30]]; // G. C. Greubel, Nov 11 2024

Mathematica

Table[2^(2*n-1)*(3^(n+1)-1),{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
CoefficientList[Series[1/((1-4x)(1-12x)),{x,0,20}],x] (* or *) LinearRecurrence[{16,-48},{1,16},20] (* Harvey P. Dale, Nov 30 2011 *)

SageMath

A016159=BinaryRecurrenceSequence(16,-48,1,16)
[A016159(n) for n in range(31)] # G. C. Greubel, Nov 11 2024

Formula

a(n) = 2^(2*n-1)*(3^(n+1)-1). - Bruno Berselli, Feb 09 2011

a(n) = 12*a(n-1) + 4^n with a(0)=1. - Vincenzo Librandi, Feb 09 2011

a(n) = 16*a(n-1) - 48*a(n-2), a(0)=1, a(1)=16. - Harvey P. Dale, Nov 30 2011

E.g.f.: (1/2)*(3*exp(12*x) - exp(4*x)). - G. C. Greubel, Nov 11 2024

Extensions

More terms added by G. C. Greubel, Nov 11 2024