A074623 a(n) = 7^n + 9^n.

2, 16, 130, 1072, 8962, 75856, 649090, 5606512, 48811522, 427774096, 3769259650, 33358386352, 296270823682, 2638754838736, 23555015527810, 210638693604592, 1886253119421442, 16909812213653776, 151723048894909570

Offset: 0

Author

Robert G. Wilson v, Aug 26 2002

Keywords

• easy
• nonn

Comments

Up to signs, the ninth inverse binomial transform of 2^n+delta(n,0), where delta is the Kronecker delta function. - John M. Campbell, Jul 29 2018

Links

• Index entries for linear recurrences with constant coefficients, signature (16,-63).

Crossrefs

Cf. A000420 (powers of 7), A001019 (powers of 9).

Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600..A074624.

Programs

Mathematica

Table[7^n + 9^n, {n, 0, 20}]
LinearRecurrence[{16,-63},{2,16},30] (* Harvey P. Dale, Aug 22 2015 *)

Formula

From Mohammad K. Azarian, Jan 11 2009: (Start)

G.f.: 1/(1-7*x) + 1/(1-9*x).

E.g.f.: exp^(7*x) + exp^(9*x). (End)

a(n) = 16*a(n-1) - 63*a(n-2) with a(0)=2, a(1)=16. - Vincenzo Librandi, Jul 21 2010

a(n) = A000420(n) + A001019(n). - Michel Marcus, Jul 30 2018