A034513 a(n) = 1^n + 3^n + 9^n.

3, 13, 91, 757, 6643, 59293, 532171, 4785157, 43053283, 387440173, 3486843451, 31381236757, 282430067923, 2541867422653, 22876797237931, 205891146443557, 1853020231898563, 16677181828806733, 150094635684419611

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

Comments

Also the sum of n-th powers of the divisors of 9.

Links

• T. D. Noe, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Crossrefs

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

Programs

Mathematica

Table[1^n + 3^n + 9^n, {n, 0, 20}]
LinearRecurrence[{13,-39,27},{3,13,91},20] (* Harvey P. Dale, Apr 13 2012 *)

PARI

a(n)=1+3^n+9^n \\ Charles R Greathouse IV, Jun 10 2011

Sage

[sigma(9,n)for n in range(0,19)] # Zerinvary Lajos, Jun 04 2009

Formula

G.f.: 1/(1-x)+1/(1-3*x)+1/(1-9*x). E.g.f.: e^x+e^(3*x)+e^(9*x). - Mohammad K. Azarian, Dec 26 2008

a(n) = 13*a(n-1) - 39*a(n-2) + 27*a(n-3), a(0)=3, a(1)=13, a(2)=91. - Harvey P. Dale, Apr 13 2012