A074543 a(n) = 2^n + 6^n + 9^n.

3, 17, 121, 953, 7873, 66857, 578161, 5063033, 44726593, 397498697, 3547251601, 31743858713, 284606322913, 2554926530537, 22955156635441, 206361317111993, 1855841298824833, 16694108359242377, 150196195253929681

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 (17,-84,108).

Crossrefs

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

Programs

Magma

[2^n + 6^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2011

Mathematica

Table[2^n + 6^n + 9^n, {n, 0, 20}]
LinearRecurrence[{17,-84,108},{3,17,121},30] (* Harvey P. Dale, Feb 20 2015 *)

Formula

From Mohammad K. Azarian, Dec 27 2008: (Start)

G.f.: 1/(1-2*x) + 1/(1-6*x) + 1/(1-9*x).

E.g.f.: exp(2*x) + exp(6*x) + exp(9*x). (End)

a(n) = 17*a(n-1) - 84*a(n-2) + 108*a(n-3); a(0)=3, a(1)=17, a(2)=121. - Harvey P. Dale, Feb 20 2015