A198396 a(n) = 6^n - 6*n.

1, 0, 24, 198, 1272, 7746, 46620, 279894, 1679568, 10077642, 60466116, 362796990, 2176782264, 13060693938, 78364164012, 470184984486, 2821109907360, 16926659444634, 101559956668308, 609359740010382, 3656158440062856, 21936950640377730, 131621703842267004, 789730223053602678

Offset: 0

Author

Vincenzo Librandi, Oct 26 2011

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. A005803, A107583, A107584, A107585.

Programs

Magma

[6^n-6*n: n in [0..25]];

Mathematica

CoefficientList[Series[(1 - 8*x + 37*x^2)/((1 - 6*x)*(1 -x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
Table[6^n-6n,{n,0,30}] (* or *) LinearRecurrence[{8,-13,6},{1,0,24},30] (* Harvey P. Dale, Jul 25 2019 *)

PARI

a(n)=6^n-6*n \\ Charles R Greathouse IV, Jul 06 2017

Formula

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

G.f.: (1-8*x+37*x^2)/((1-6*x)*(1-x)^2). - Vincenzo Librandi, Jan 04 2013

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