A003263 Number of representations of n as a sum of distinct Lucas numbers 1, 3, 4, 7, 11, ... (A000204). (Formerly M0045)

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

1,4

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

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.

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

Cf. A054770, A000204.

Sequence in context: A334153 A281461 A146973 * A271224 A157242 A281423

Adjacent sequences: A003260 A003261 A003262 * A003264 A003265 A003266

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, May 29 2000

Status

approved