A074608 a(n) = 3^n + 7^n.

2, 10, 58, 370, 2482, 17050, 118378, 825730, 5771362, 40373290, 282534298, 1977503890, 13841818642, 96890604730, 678227855818, 4747575858850, 33232973616322, 232630643127370, 1628413985330938, 11398896347634610

Offset: 0

Author

Robert G. Wilson v, Aug 25 2002

Keywords

• easy
• nonn

Links

• G. C. Greubel and Jon E. Schoenfield, Table of n, a(n) for n = 0..1000 (terms 0..160 from G. C. Greubel).
• Index entries for linear recurrences with constant coefficients, signature (10,-21).

Crossrefs

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

Cf. A081336.

Programs

Mathematica

Table[3^n + 7^n, {n, 0, 25}]
RecurrenceTable[{a[0]== 2, a[1]== 10, a[n]== 10*a[n-1]  - 21*a[n-2]}, a, {n,30}] (* G. C. Greubel, Aug 20 2015 *)

PARI

first(m)=vector(m,i,i--;3^i + 7^i) \\ Anders Hellström, Aug 20 2015

PARI

Vec(1/(1-3*x) + 1/(1-7*x) + O(x^50)) \\ Altug Alkan, Oct 12 2015

Formula

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

G.f.: 1/(1-3*x) + 1/(1-7*x).

E.g.f.: exp(3*x) + exp(7*x). (End)

a(n) = 10*a(n-1)-21*a(n-2) with a(0)=2, a(1)=10. - Vincenzo Librandi, Jul 21 2010

a(n) = 2 * A081336(n). - Michel Marcus, Oct 07 2015