A016190 Expansion of 1/((1-9x)(1-11x)).

1, 20, 301, 4040, 51001, 620060, 7352101, 85656080, 985263601, 11225320100, 126965305501, 1427999420120, 15990423157801, 178436520564140, 1985678518660501, 22048354837360160, 244384923399813601

Offset

0,2

Comments

a(n-1), n >= 0, with a(-1) = 0, is also the number of words of length n, over an alphabet of eleven letters, of which any chosen one appears an odd number of times. See the Jul 22 2003 comment in A006516 (4-letter case) and the Balakrishnan reference there. - Wolfdieter Lang, Jul 18 2017

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (20,-99).

Formula

a(n) = (11^(n+1)-9^(n+1))/2. - Bruno Berselli, Feb 09 2011

From Vincenzo Librandi, Feb 09 2011: (Start)

a(n) = 11*a(n-1)+9^n, a(0)=1.

a(n) = 20*a(n-1)-99*a(n-2), a(0)=1, a(1)=20. (End)

Mathematica

CoefficientList[Series[1/((1-9x)(1-11x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{20, -99}, {1, 20}, 20] (* Harvey P. Dale, Jun 27 2017 *)

Prog

(PARI) Vec(1/((1-9*x)*(1-11*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A006516, A081203.

Sequence in context: A004345 A001755 A361577 * A016188 A006300 A282372

Adjacent sequences: A016187 A016188 A016189 * A016191 A016192 A016193

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved