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A003263
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Number of representations of n as a sum of distinct Lucas numbers 1, 3, 4, 7, 11, ... (A000204).
(Formerly M0045)
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35
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1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 3, 2, 0, 2, 3, 1, 0, 3, 3, 0, 2, 4, 2, 0, 3, 3, 0, 1, 4, 3, 0, 3, 5, 2, 0, 4, 4, 0, 2, 5, 3, 0, 3, 4, 1, 0, 4, 4, 0, 3, 6, 3, 0, 5, 5, 0, 2, 6, 4, 0, 4, 6, 2, 0, 5, 5, 0, 3, 6, 3, 0, 4, 4, 0, 1, 5, 4, 0, 4, 7, 3, 0, 6, 6, 0, 3, 8, 5, 0, 5, 7, 2, 0, 6, 6, 0, 4, 8, 4, 0, 6, 6, 0, 2, 7
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OFFSET
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1,4
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REFERENCES
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A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 58.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MATHEMATICA
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n1 = 10; n2 = LucasL[n1]; Product[1 + x^LucasL[n], {n, 1, n1}] + O[x]^n2 // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Feb 17 2017, after Joerg Arndt *)
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PROG
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(PARI)
L(n)=fibonacci(n+1) + fibonacci(n-1);
N = 66; x = 'x + O('x^N);
gf = prod(n=1, 11, 1 + x^L(n) );
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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