A245806 a(n) = 3^n + 10^n.
2, 13, 109, 1027, 10081, 100243, 1000729, 10002187, 100006561, 1000019683, 10000059049, 100000177147, 1000000531441, 10000001594323, 100000004782969, 1000000014348907, 10000000043046721, 100000000129140163, 1000000000387420489, 10000000001162261467
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (13,-30).
Crossrefs
Programs
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Magma
[3^n+10^n: n in [0..25]];
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Magma
I:=[2,13]; [n le 2 select I[n] else 13*Self(n-1)-30*Self(n-2): n in [1..25]];
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Mathematica
Table[(3^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 13 x)/((1 - 3 x) (1 - 10 x)), {x, 0, 30}], x] -
PARI
a(n)=3^n + 10^n \\ Charles R Greathouse IV, Aug 26 2014
Formula
G.f.: (2-13*x)/((1-3*x)(1-10*x)).
E.g.f.: e^(3*x) + e^(10*x).
a(n) = 13*a(n-1)-30*a(n-2) for n>1.