A199560 a(n) = (3*9^n + 1)/2.
2, 14, 122, 1094, 9842, 88574, 797162, 7174454, 64570082, 581130734, 5230176602, 47071589414, 423644304722, 3812798742494, 34315188682442, 308836698141974, 2779530283277762, 25015772549499854, 225141952945498682, 2026277576509488134, 18236498188585393202
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (10,-9).
Programs
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Magma
[(3*9^n+1)/2: n in [0..30]];
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Mathematica
LinearRecurrence[{10,-9},{2,14},30] (* or *) NestList[9#-4&,2,30] (* Harvey P. Dale, May 30 2012 *)
Formula
a(n) = 2*A066443(n).
a(n) = 9*a(n-1) - 4.
a(n) = 10*a(n-1) - 9*a(n-2).
G.f.: 2*(1-3*x)/((1-x)*(1-9*x)).
From Elmo R. Oliveira, Sep 13 2024: (Start)
E.g.f.: exp(x)*(3*exp(8*x) + 1)/2.
a(n) = A199561(n)/2. (End)