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Search: id:A056573
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| 0, 1, 1, 64, 729, 15625, 262144, 4826809, 85766121, 1544804416, 27680640625, 496981290961, 8916100448256, 160005726539569, 2871098559212689, 51520374361000000, 924491486192068809, 16589354847268067929
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OFFSET
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0,4
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REFERENCES
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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).
J. Riordan, Generating functions for powers of Fibonacci numbers, Duke. Math. J. 29 (1962) 5-1.
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FORMULA
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a(n)= F(n)^6, F(n)=A000045(n).
G.f.: x*p(6, x)/q(6, x) with p(6, x) := sum(A056588(5, m)*x^m, m=0..5)= (1-x)*(1-11*x-64*x^2-11*x^3+x^4) and q(6, x) := sum(A055870(7, m)*x^m, m=0..7) = (1+x)*(1-3*x+x^2)*(1+7*x+x^2)*(1-18*x+x^2) (denominator factorization deduced from Riordan result).
Recursion (cf. Knuth's exercise): sum(A055870(7, m)*a(n-m), m=0..7) = 0, n >= 7; inputs: a(n), n=0..6.
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CROSSREFS
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Cf. A000045, A007598, A056570-2, A056588, A055870.
Sixth row of array A103323.
Sequence in context: A046455 A092758 A030516 this_sequence A108538 A055867 A027003
Adjacent sequences: A056570 A056571 A056572 this_sequence A056574 A056575 A056576
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 10 2000
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