A173657 2+2^n+3^n.

4, 7, 15, 37, 99, 277, 795, 2317, 6819, 20197, 60075, 179197, 535539, 1602517, 4799355, 14381677, 43112259, 129271237, 387682635, 1162785757, 3487832979, 10462450357, 31385253915, 94151567437, 282446313699, 847322163877, 2541932937195, 7625731702717

Offset: 0

Author

Gary Detlefs, Nov 24 2010

Keywords

• nonn
• easy

Comments

Sum of the n-th powers of the first 5 Fibonacci numbers A000045(0..4).

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A075996 (primes), A007689.

Programs

Maple

with(combinat):f:=n-> sum(fibonacci(k)^n,k=0..4):seq(f(n),n=1..20);

Mathematica

Table[2+2^n+3^n,{n,0,40}] (* or *) LinearRecurrence[{6,-11,6},{4,7,15},40](* Harvey P. Dale, Jun 08 2011 *)

Formula

a(n)= 6*a(n-1)-11*a(n-2)+6*a(n-3).

a(n) = 1+A001550(n).

G.f.: ( -4+17*x-17*x^2 ) / ( (x-1)*(3*x-1)*(2*x-1) ).

Extensions

More terms from Harvey P. Dale, Jun 08 2011