OFFSET
0,3
FORMULA
a(n) <= A304705(n).
EXAMPLE
n | Partition (d1,d2,...,dm) | (d1/1, d2/2, ... , dm/m)
--+-----------------------------+---------------------------------------------
1 | (1) | (1)
2 | (2) | (2)
| (1, 1) | (1, 1/2)
3 | (3) | (3)
| (1, 1, 1) | (1, 1/2, 1/3)
4 | (4) | (4)
| (2, 2) | (2, 1)
| (1, 1, 1, 1) | (1, 1/2, 1/3, 1/4)
5 | (5) | (5)
| (2, 3) | (2, 3/2)
| (1, 1, 1, 1, 1) | (1, 1/2, 1/3, 1/4, 1/5)
6 | (6) | (6)
| (3, 3) | (3, 3/2)
| (2, 2, 2) | (2, 1, 2/3)
| (1, 1, 1, 1, 1, 1) | (1, 1/2, 1/3, 1/4, 1/5, 1/6)
7 | (7) | (7)
| (3, 4) | (3, 2)
| (1, 1, 1, 1, 1, 1, 1) | (1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7)
8 | (8) | (8)
| (3, 5) | (3, 5/2)
| (4, 4) | (4, 2/1)
| (2, 3, 3) | (2, 3/2, 1)
| (2, 2, 2, 2) | (2, 1, 2/3, 1/2)
| (1, 1, 1, 1, 1, 1, 1, 1) | (1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8)
9 | (9) | (9)
| (4, 5) | (4, 5/2)
| (2, 3, 4) | (2, 3/2, 4/3)
| (3, 3, 3) | (3, 3/2, 1)
| (1, 1, 1, 1, 1, 1, 1, 1, 1) | (1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9)
MAPLE
b:= proc(n, r, i, t) option remember; `if`(n=0, 1, `if`(i>n, 0,
b(n, r, i+1, t)+`if`(i/t>=r, 0, b(n-i, i/t, i, t+1))))
end:
a:= n-> b(n, n+1, 1$2):
seq(a(n), n=0..80); # Alois P. Heinz, May 17 2018
MATHEMATICA
b[n_, r_, i_, t_] := b[n, r, i, t] = If[n == 0, 1, If[i > n, 0, b[n, r, i + 1, t] + If[i/t >= r, 0, b[n - i, i/t, i, t + 1]]]];
a[n_] := b[n, n + 1, 1, 1];
a /@ Range[0, 80] (* Jean-François Alcover, Nov 23 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 17 2018
STATUS
approved