A016178 Expansion of g.f. 1/((1 - 7x)*(1 - 9x)).
1, 16, 193, 2080, 21121, 206896, 1979713, 18640960, 173533441, 1602154576, 14701866433, 134294124640, 1222488408961, 11099284691056, 100571785292353, 909893629141120, 8222275592839681, 74233110849544336, 669726411243809473, 6038936596379658400, 54430221633714537601
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (16,-63).
Programs
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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 *) -
PARI
a(n)=(9^n++-7^n)/2 \\ Charles R Greathouse IV, Sep 24 2012
Formula
a(n) = (9^(n+1) - 7^(n+1))/2 = A081202(n+1). Binomial transform of A081034. - R. J. Mathar, Sep 18 2008
From Vincenzo Librandi, Feb 09 2011: (Start)
a(n) = 9*a(n-1) + 7^n, with a(0)=1.
a(n) = 16*a(n-1) - 63*a(n-2), n >= 2. (End)
E.g.f.: exp(7*x)*(9*exp(2*x) - 7)/2. - Stefano Spezia, Jul 23 2024
Extensions
a(18)-a(20) from Stefano Spezia, Jul 23 2024