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%I #20 Apr 23 2022 22:17:08
%S 4,7,15,37,99,277,795,2317,6819,20197,60075,179197,535539,1602517,
%T 4799355,14381677,43112259,129271237,387682635,1162785757,3487832979,
%U 10462450357,31385253915,94151567437,282446313699,847322163877,2541932937195,7625731702717
%N 2+2^n+3^n.
%C Sum of the n-th powers of the first 5 Fibonacci numbers A000045(0..4).
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F a(n)= 6*a(n-1)-11*a(n-2)+6*a(n-3).
%F a(n) = 1+A001550(n).
%F G.f.: ( -4+17*x-17*x^2 ) / ( (x-1)*(3*x-1)*(2*x-1) ).
%p with(combinat):f:=n-> sum(fibonacci(k)^n,k=0..4):seq(f(n),n=1..20);
%t Table[2+2^n+3^n,{n,0,40}] (* or *) LinearRecurrence[{6,-11,6},{4,7,15},40](* _Harvey P. Dale_, Jun 08 2011 *)
%Y Cf. A075996 (primes), A007689.
%K nonn,easy
%O 0,1
%A _Gary Detlefs_, Nov 24 2010
%E More terms from _Harvey P. Dale_, Jun 08 2011
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