A221908 a(n) = 6^n + 6*n.

1, 12, 48, 234, 1320, 7806, 46692, 279978, 1679664, 10077750, 60466236, 362797122, 2176782408, 13060694094, 78364164180, 470184984666, 2821109907552, 16926659444838, 101559956668524, 609359740010610, 3656158440063096, 21936950640377982, 131621703842267268

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-13,6).

Formula

G.f.: (1+4*x-35*x^2)/((1-x)^2*(1-6*x)).

a(n) = 8*a(n-1) - 13*a(n-2) + 6*a(n-3).

E.g.f.: exp(x)*(exp(5*x) + 6*x). - Elmo R. Oliveira, Sep 10 2024

Mathematica

Table[(6^n + 6 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 4 x - 35 x^2)/((1 - x)^2 (1 - 6 x)), {x, 0, 30}], x]

Prog

(Magma) [6^n+6*n: n in [0..30]]; /* or */ I:=[1, 12, 48]; [n le 3 select I[n] else 8*Self(n-1)-13*Self(n-2)+6*Self(n-3): n in [1..30]];
(PARI) a(n)=6^n+6*n \\ Charles R Greathouse IV, Apr 18 2013

Crossrefs

Cf. A198396.

Sequence in context: A007200 A061148 A339760 * A242026 A340727 A052601

Adjacent sequences: A221905 A221906 A221907 * A221909 A221910 A221911

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2013

Status

approved