A226200 a(n) = 6^n + n.
1, 7, 38, 219, 1300, 7781, 46662, 279943, 1679624, 10077705, 60466186, 362797067, 2176782348, 13060694029, 78364164110, 470184984591, 2821109907472, 16926659444753, 101559956668434, 609359740010515, 3656158440062996, 21936950640377877, 131621703842267158, 789730223053602839
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (8,-13,6).
Crossrefs
Programs
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Magma
[6^n+n: n in [0..30]];
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Magma
I:=[1, 7, 38]; [n le 3 select I[n] else 8*Self(n-1)-13*Self(n-2)+6*Self(n-3): n in [1..30]];
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Mathematica
Table[6^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(-1 + x + 5 x^2) / ((6 x - 1) (x - 1)^2), {x, 0, 30}], x] -
PARI
a(n)=6^n+n \\ Charles R Greathouse IV, Oct 07 2015
Formula
G.f.: (-1+x+5*x^2)/((6*x-1)*(x-1)^2).
a(n) = 8*a(n-1) - 13*a(n-2) + 6*a(n-3).
E.g.f.: exp(x)*(exp(5*x) + x). - Elmo R. Oliveira, Mar 05 2025
Comments