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Search: id:A000121
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| A000121 |
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Number of representations of n as a sum of Fibonacci numbers (1 is allowed twice as a part).
(Formerly M0249 N0088)
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+0
7
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| 1, 2, 2, 3, 3, 3, 4, 3, 4, 5, 4, 5, 4, 4, 6, 5, 6, 6, 5, 6, 4, 5, 7, 6, 8, 7, 6, 8, 6, 7, 8, 6, 7, 5, 5, 8, 7, 9, 9, 8, 10, 7, 8, 10, 8, 10, 8, 7, 10, 8, 9, 9, 7, 8, 5, 6, 9, 8, 11, 10, 9, 12, 9, 11, 13, 10, 12, 9, 8, 12, 10, 12, 12, 10, 12, 8, 9, 12, 10, 13, 11, 9, 12, 9, 10, 11, 8, 9, 6, 6, 10, 9
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of partitions into distinct Fibonacci parts (1 counted as two distinct Fibonacci numbers).
Inverse Euler transform of sequence has generating function sum_{n>0} x^F(n)-x^{2F(n)} where F() is Fibonacci.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
D. A. Klarner, Representations of N as a sum of distinct elements from special sequences, Fib. Quart., 4 (1966), 289-306 and 322.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..6765
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MAPLE
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with(combinat): p := product((1+x^fibonacci(i)), i=1..25): s := series(p, x, 1000): for k from 0 to 250 do printf(`%d, `, coeff(s, x, k)) od:
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PROGRAM
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(PARI) a(n)=local(A, m, f); if(n<0, 0, A=1+x*O(x^n); m=1; while((f=fibonacci(m))<=n, A*=1+x^f; m++); polcoeff(A, n))
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CROSSREFS
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Cf. A000119. Least inverse is A083853.
Adjacent sequences: A000118 A000119 A000120 this_sequence A000122 A000123 A000124
Sequence in context: A072789 A126302 A134674 this_sequence A049846 A086712 A125842
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 18 2000
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