A074515 a(n) = 1^n + 4^n + 9^n.

3, 14, 98, 794, 6818, 60074, 535538, 4799354, 43112258, 387682634, 3487832978, 31385253914, 282446313698, 2541932937194, 22877060890418, 205892205836474, 1853024483819138, 16677198879535754, 150094704016475858

Offset: 0

Author

Robert G. Wilson v, Aug 23 2002

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (14,-49,36).

Crossrefs

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

Cf. A052539.

Programs

Mathematica

Table[1^n + 4^n + 9^n, {n, 0, 20}]
LinearRecurrence[{14,-49,36},{3,14,98},30] (* Harvey P. Dale, Aug 06 2013 *)

Python

def a(n): return 1 + 4**n + 9**n
print([a(n) for n in range(19)]) # Michael S. Branicky, Mar 14 2021

Formula

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

G.f.: 1/(1-x) + 1/(1-4*x) + 1/(1-9*x).

E.g.f.: e^x + e^(4*x) + e^(9*x). (End)

a(n) = 13*a(n-1) - 36*a(n-2) + 24 with a(0)=3, a(1)=14. - Vincenzo Librandi, Jul 21 2010