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A016190
Expansion of 1/((1-9x)(1-11x)).
4
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
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
Sequence in context: A004345 A001755 A361577 * A016188 A006300 A282372
KEYWORD
nonn,easy
STATUS
approved