A199566 a(n) = (7*9^n + 1)/2.
4, 32, 284, 2552, 22964, 206672, 1860044, 16740392, 150663524, 1355971712, 12203745404, 109833708632, 988503377684, 8896530399152, 80068773592364, 720618962331272, 6485570660981444, 58370135948832992, 525331223539496924, 4727981011855472312, 42551829106699250804
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
[(7*9^n+1)/2: n in [0..30]];
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Mathematica
(7*9^Range[0,20]+1)/2 (* or *) LinearRecurrence[{10,-9},{4,32},20] (* Harvey P. Dale, Dec 08 2012 *)
Formula
a(n) = 4*A187709(n).
a(n) = 9*a(n-1) - 4 for n > 0.
a(n) = 10*a(n-1) - 9*a(n-2) for n > 1.
G.f.: 4*(1-2*x)/((1-x)*(1-9*x)).
From Elmo R. Oliveira, Aug 23 2024: (Start)
E.g.f.: exp(x)*(7*exp(8*x) + 1)/2.
a(n) = A199567(n)/2. (End)