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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A006516, A081203.

Programs

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 *)

PARI

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

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)