A074579 a(n) = 6^n + 8^n + 9^n.

3, 23, 181, 1457, 11953, 99593, 840241, 7160057, 61503553, 531715913, 4620992401, 40333791257, 353325795553, 3104682336233, 27353203130161, 241545689168057, 2137316275469953, 18945908172796553, 168210593763149521

Offset: 0

Author

Robert G. Wilson v, Aug 23 2002

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (23,-174,432).

Crossrefs

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

Programs

Magma

[6^n + 8^n + 9^n: n in [0..20]]; // Vincenzo Librandi, May 20 2011

Mathematica

Table[6^n + 8^n + 9^n, {n, 0, 20}]
LinearRecurrence[{23,-174,432},{3,23,181},30] (* Harvey P. Dale, Sep 20 2016 *)

Formula

From Mohammad K. Azarian, Dec 26 2008: (Start)

G.f.: 1/(1-6*x) + 1/(1-8*x) + 1/(1-9*x).

E.g.f.: e^(6*x) + e^(8*x) + e^(9*x). (End)

a(n) = 23*a(n-1)-174*a(n-2)+432*a(n-3). - Wesley Ivan Hurt, Apr 17 2022