A221905 a(n) = 3^n + 3*n.
1, 6, 15, 36, 93, 258, 747, 2208, 6585, 19710, 59079, 177180, 531477, 1594362, 4783011, 14348952, 43046769, 129140214, 387420543, 1162261524, 3486784461, 10460353266, 31381059675, 94143178896, 282429536553, 847288609518, 2541865828407, 7625597485068, 22876792455045
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-7,3).
Programs
-
Magma
[3^n+3*n: n in [0..30]];
-
Magma
I:=[1, 6, 15]; [n le 3 select I[n] else 5*Self(n-1)-7*Self(n-2)+3*Self(n-3): n in [1..30]];
-
Mathematica
Table[(3^n + 3 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + x - 8 x^2)/((1 - x)^2 (1 -3 x)), {x, 0, 30}], x]
Formula
G.f.: (1 + x - 8*x^2)/((1-x)^2*(1-3*x)).
a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).
a(n) = A176805(n) - 1.
E.g.f.: exp(x)*(exp(2*x) + 3*x). - Elmo R. Oliveira, Sep 10 2024