A063270 a(n) = 9^(2*n) + 1.
2, 82, 6562, 531442, 43046722, 3486784402, 282429536482, 22876792454962, 1853020188851842, 150094635296999122, 12157665459056928802, 984770902183611232882, 79766443076872509863362, 6461081889226673298932242, 523347633027360537213511522, 42391158275216203514294433202
Offset: 0
Links
- Harry J. Smith, Table of n, a(n) for n = 0..100
- Index entries for linear recurrences with constant coefficients, signature (82,-81).
Programs
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Mathematica
9^(2*Range[0,20])+1 (* or *) LinearRecurrence[{82,-81},{2,82},20] (* Harvey P. Dale, Jul 31 2013 *) -
PARI
a(n) = 9^(2*n) + 1;
Formula
a(n) = 82*a(n-1) - 81*a(n-2), a(0)=2, a(1)=82. - Harvey P. Dale, Jul 31 2013
From Elmo R. Oliveira, Jun 16 2025: (Start)
G.f.: 2*(1-41*x)/((x-1)*(81*x-1)).
E.g.f.: exp(x)*(exp(80*x) + 1).
a(n) = A062396(2*n). (End)
Extensions
More terms from Harvey P. Dale, Jul 31 2013