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

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

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (14,-48)

Formula

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

a(n) = 4*8^n-3*6^n = A081201(n+1). Binomial transform of A081033. [R. J. Mathar, Sep 18 2008]

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]

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 *)

Prog

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

Crossrefs

Cf. A081033, A081201.

Sequence in context: A002451 A302994 A207259 * A081201 A065899 A162965

Adjacent sequences: A016167 A016168 A016169 * A016171 A016172 A016173

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved