A003263 Number of representations of n as a sum of distinct Lucas numbers 1, 3, 4, 7, 11, ... (A000204).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• T. D. Noe, Table of n, a(n) for n = 1..9349
• 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.

Crossrefs

Cf. A054770, A000204.

Programs

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 *)

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

Formula

G.f.: Product_{n>=1} (1 + x^L(n)) where L(n) = A000204(n). - Joerg Arndt, Jul 14 2013

Extensions

More terms from James Sellers, May 29 2000