OFFSET
0,8
COMMENTS
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..5000
FORMULA
EXAMPLE
G.f.: A(x) = 1 + x^2 + x^4 + x^5 + x^6 + 2*x^7 + x^8 + 2*x^9 + 3*x^10 +...
where the g.f. may be expressed by the product:
A(x) = 1/((1-x^2)*(1-x^5)*(1-x^7)*(1-x^10)*(1-x^13)*...)
in which the exponents of x are the upper Wythoff numbers (A001950):
[2,5,7,10,13,15,18,20,23,26,28,31,34,36,39,41,44,47,49,52,54,57,60,...].
a(12) counts these partitions: [10,2], [7,5], [5,5,2], [2,2,2,2,2,2]. Clark Kimberling, Mar 09 2014
MATHEMATICA
t = Table[Floor[n+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, PWU=1/prod(m=1, ceil(n/phi), 1-x^floor(m*phi^2)+x*O(x^n))); polcoeff(PWU, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 25 2011
STATUS
approved