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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

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

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]

Prog

(Magma) [3^n+3*n: n in [0..30]]; /* or */ 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]];

Crossrefs

Cf. A107583, A176805, A370658.

Sequence in context: A128443 A245470 A135854 * A083011 A299267 A254008

Adjacent sequences: A221902 A221903 A221904 * A221906 A221907 A221908

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2013

Status

approved