A074546 a(n) = 2^n + 8^n + 9^n.

3, 19, 149, 1249, 10673, 91849, 793649, 6880249, 59824193, 521638729, 4560527249, 39970996249, 351149017313, 3091621650409, 27274838982449, 241075504216249, 2134495165628033, 18928981513482889, 168109033806743249

Offset: 0

Author

Robert G. Wilson v, Aug 23 2002

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (19,-106,144).

Crossrefs

Cf. A001550, A001576, A034513, A001579, A074501 - A074580.

Programs

Magma

[ 2^n + 8^n + 9^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011

Mathematica

Table[2^n + 8^n + 9^n, {n, 0, 20}]
LinearRecurrence[{19,-106,144},{3,19,149},20] (* Harvey P. Dale, May 31 2013 *)

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)

G.f.: 1/(1-2*x) + 1/(1-8*x) + 1/(1-9*x).

E.g.f.: exp(2*x) + exp(8*x) + exp(9*x). (End)

a(n) = 19*a(n-1) - 106*a(n-2) + 144*a(n-3).