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

Author

Vincenzo Librandi, Mar 02 2013

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-13,6).

Crossrefs

Cf. A198396.

Programs

Magma

[6^n+6*n: n in [0..30]];

Magma

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]];

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]

PARI

a(n)=6^n+6*n \\ Charles R Greathouse IV, Apr 18 2013

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