A188165 a(n) = 2^n + 9.
10, 11, 13, 17, 25, 41, 73, 137, 265, 521, 1033, 2057, 4105, 8201, 16393, 32777, 65545, 131081, 262153, 524297, 1048585, 2097161, 4194313, 8388617, 16777225, 33554441, 67108873, 134217737, 268435465, 536870921, 1073741833, 2147483657, 4294967305
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-2).
Programs
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Magma
[2^n+9: n in [0..40]]; // Vincenzo Librandi, May 13 2014
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Mathematica
Table[2^n + 9, {n, 0, 40}] (* or *) CoefficientList[Series[(10 - 19 x)/((1 - x) (1 - 2 x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2014 *) -
PARI
a(n) = 1<
Michel Marcus, Jul 19 2013
Formula
From Bruno Berselli, Sep 26 2011: (Start)
G.f.: (10-19*x)/(1-3*x+2*x^2).
a(n) = 2*a(n-1)-9 = 3*a(n-1)-2*a(n-2).
a(n) = A168415(n)+2. (End)
E.g.f.: exp(2*x) + 9*exp(x). - Elmo R. Oliveira, Nov 08 2023