A155613 8^n - 3^n + 1.

1, 6, 56, 486, 4016, 32526, 261416, 2094966, 16770656, 134198046, 1073682776, 8589757446, 68718945296, 549754219566, 4398041728136, 35184357739926, 281474933663936, 2251799684545086, 18014398122061496, 144115186913594406

Offset: 0

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (12,-35,24).

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612.

Programs

Mathematica

Table[8^n-3^n+1,{n,0,20}] (* or *) LinearRecurrence[{12,-35,24},{1,6,56},20] (* Harvey P. Dale, Mar 12 2014 *)

PARI

a(n)=8^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 1/(1-8*x)-1/(1-3*x)+1/(1-x).

E.g.f.: e^(8*x)-e^(3*x)+e^x.

a(n) = 11*a(n-1)-24*a(n-2)+14 with a(0)=1, a(1)=6. - Vincenzo Librandi, Jul 21 2010