OFFSET
0,4
COMMENTS
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..5000
FORMULA
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + 8*x^8 +...
where the g.f. may be expressed by the product:
A(x) = 1/((1-x^1)*(1-x^3)*(1-x^4)*(1-x^6)*(1-x^8)*...)
in which the exponents of x are the lower Wythoff numbers (A000201):
[1,3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,29,30,32,33,35,37,38,40,...].
a(7) counts these partitions: 61, 43, 4111, 331, 31111, 1111111. Clark Kimberling, Mar 09 2014
MATHEMATICA
t = Table[Floor[n*GoldenRatio], {n, 1, 200}]; p[n_] := IntegerPartitions[n, All, t]; Table[ p[n], {n, 0, 12}] (*shows partitions*)
a[n_] := Length@p@n; a /@ Range[0, 80]
(* Clark Kimberling, Mar 09 2014 *)
PROG
(PARI) {a(n)=local(phi=(sqrt(5)+1)/2, PWL=1/prod(m=1, ceil(n/phi), 1-x^floor(m*phi)+x*O(x^n))); polcoeff(PWL, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 25 2011
STATUS
approved