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

0,1

Comments

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

Links

Table of n, a(n) for n=0..27.

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

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) ).

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 *)

Crossrefs

Cf. A075996 (primes), A007689.

Sequence in context: A145970 A232048 A145795 * A213358 A065935 A361975

Adjacent sequences: A173654 A173655 A173656 * A173658 A173659 A173660

Keyword

nonn,easy

Author

Gary Detlefs, Nov 24 2010

Extensions

More terms from Harvey P. Dale, Jun 08 2011

Status

approved