A016178 Expansion of 1/((1-7x)(1-9x)).

1, 16, 193, 2080, 21121, 206896, 1979713, 18640960, 173533441, 1602154576, 14701866433, 134294124640, 1222488408961, 11099284691056, 100571785292353, 909893629141120, 8222275592839681, 74233110849544336

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (16,-63)

Formula

a(n) = (9^(n+1) - 7^(n+1))/2 = A081202(n+1). Binomial transform of A081034. - R. J. Mathar, Sep 18 2008

a(n) = 9*a(n-1) + 7^n, with a(0)=1. - Vincenzo Librandi, Feb 09 2011

a(n) = 16*a(n-1) - 63*a(n-2), n >= 2. - Vincenzo Librandi, Feb 09 2011

Mathematica

Join[{a=1, b=16}, Table[c=16*b-63*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
CoefficientList[Series[1/((1-7x)(1-9x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {16, -63}, {1, 16}, 30] (* Harvey P. Dale, Mar 11 2013 *)

Prog

(PARI) a(n)=(9^n++-7^n)/2 \\ Charles R Greathouse IV, Sep 24 2012

Crossrefs

Sequence in context: A338100 A218176 A120994 * A081202 A196803 A292785

Adjacent sequences: A016175 A016176 A016177 * A016179 A016180 A016181

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved