A016170 Expansion of 1/((1-6*x)*(1-8*x)).

1, 14, 148, 1400, 12496, 107744, 908608, 7548800, 62070016, 506637824, 4113568768, 33271347200, 268347559936, 2159841173504, 17357093552128, 139326933401600, 1117436577120256, 8956419276406784, 71752914167922688

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14,-48).

Crossrefs

Cf. A081033, A081201, A016129.

Programs

Magma

[n le 2 select 14^(n-1) else 14*Self(n-1) -48*Self(n-2): n in [1..31]]; // G. C. Greubel, Nov 10 2024

Maple

A016170:=n->4*8^n-3*6^n: seq(A016170(n), n=0..30); # Wesley Ivan Hurt, May 03 2017

Mathematica

CoefficientList[Series[1/((1-6x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{14,-48},{1,14},30] (* Harvey P. Dale, Dec 08 2011 *)

PARI

Vec(1/((1-6*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012

SageMath

A016170=BinaryRecurrenceSequence(14,-48,1,14)
[A016170(n) for n in range(31)] # G. C. Greubel, Nov 10 2024

Formula

a(n) = Sum_{k=1..n} 2^(n-1)*3^(n-k)*binomial(n,k). - Zerinvary Lajos, Sep 24 2006

From R. J. Mathar, Sep 18 2008: (Start)

a(n) = 4*8^n - 3*6^n = A081201(n+1).

Binomial transform of A081033. (End)

a(n) = 8*a(n-1) + 6^n. - Vincenzo Librandi, Feb 09 2011

a(0)=1, a(1)=14, a(n) = 14*a(n-1) - 48*a(n-2). - Harvey P. Dale, Dec 08 2011

E.g.f.: 4*exp(8*x) - 3*exp(6*x). - G. C. Greubel, Nov 10 2024