A221906 a(n) = 4^n + 4*n.
1, 8, 24, 76, 272, 1044, 4120, 16412, 65568, 262180, 1048616, 4194348, 16777264, 67108916, 268435512, 1073741884, 4294967360, 17179869252, 68719476808, 274877907020, 1099511627856, 4398046511188, 17592186044504, 70368744177756, 281474976710752, 1125899906842724
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-9,4).
Programs
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Magma
[4^n + 4*n: n in [0..30]];
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Magma
I:=[1, 8, 24]; [n le 3 select I[n] else 6*Self(n-1)-9*Self(n-2)+4*Self(n-3): n in [1..30]];
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Mathematica
Table[(4^n + 4 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 2 x - 15 x^2)/((1 - x)^2 (1 - 4 x)), {x, 0, 30}], x]
Formula
G.f.: (1 + 2*x - 15*x^2)/((1-x)^2*(1-4*x)).
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).
E.g.f.: exp(x)*(exp(3*x) + 4*x). - Elmo R. Oliveira, Sep 10 2024