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A003263 Number of representations of n as a sum of distinct Lucas numbers 1, 3, 4, 7, 11, ... (A000204).
(Formerly M0045)
35
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
REFERENCES
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).
LINKS
Alfred Brousseau, Fibonacci and Related Number Theoretic Tables, Fibonacci Association, San Jose, CA, 1972. See p. 58.
Casey Mongoven, Sonification of multiple Fibonacci-related sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.
FORMULA
G.f.: Product_{n>=1} (1 + x^L(n)) where L(n) = A000204(n). - Joerg Arndt, Jul 14 2013
MATHEMATICA
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 *)
PROG
(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) );
Vec(gf) \\ Joerg Arndt, Jul 14 2013
CROSSREFS
Sequence in context: A334153 A281461 A146973 * A271224 A157242 A281423
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, May 29 2000
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)