0,4

J. Riordan, Generating functions for powers of Fibonacci numbers, Duke. Math. J. 29 (1962) 5-1.

A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 1, p. 85, (exercise 1.2.8. Nr. 30) and p. 492 (solution).

a(n)= F(n)^5, F(n)=A000045(n).

G.f.: x*p(5, x)/q(5, x) with p(5, x) := sum(A056588(4, m)*x^m, m=0..4)= 1-7*x-16*x^2+7*x^3+x^4 and q(5, x) := sum(A055870(6, m)*x^m, m=0..6)= 1-8*x-40*x^2+60*x^3+40*x^4-8*x^5-x^6 = (1-x-x^2)*(1+4*x-x^2)*)*(1-11*x-x^2) (factorization deduced from Riordan result).

Recursion (cf. Knuth's exercise): sum(A055870(6, m)*a(n-m), m=0..6) = 0, n >= 6; inputs: a(n), n=0..5.

with (combinat):seq(mul(fibonacci(n), k=1..5), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 21 2007

Table[f=Fibonacci[n]; f^5, {n, 0, 12}] (Vladimir Orlovsky, Jul 22 2008)

Cf. A000045, A007598, A056570-1, A056588, A055870.

Fifth row of array A103323.

Sequence in context: A113850 A046454 A050997 this_sequence A096960 A134846 A066392

Adjacent sequences: A056569 A056570 A056571 this_sequence A056573 A056574 A056575

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 10 2000