OFFSET
0,2
COMMENTS
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.
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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 = 0..6765
Zai-Qiao Bai and Steven R. Finch, Fibonacci and Lucas Representations, Fibonacci Quart. 54 (2016), no. 4, 319-326. See Table 1 p. 324.
D. A. Klarner, Representations of N as a sum of distinct elements from special sequences, part 1, part 2, Fib. Quart., 4 (1966), 289-306 and 322.
Scott V. Tezlaf, On ordinal dynamics and the multiplicity of transfinite cardinality, arXiv:1806.00331 [math.NT], 2018. See p. 45.
FORMULA
MAPLE
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:
MATHEMATICA
imax = 20; p = Product[1+x^Fibonacci[i], {i, 1, imax}]; CoefficientList[p, x][[1 ;; Fibonacci[imax]+1]] (* Jean-François Alcover, Feb 04 2016, adapted from Maple *)
nmax = 91; s=Total/@Subsets[Select[Table[Fibonacci[i], {i, nmax}], # <= nmax &]];
Table[Count[s, n], {n, 0, nmax}] (* Robert Price, Aug 17 2020 *)
PROG
(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))
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Jun 18 2000
STATUS
approved