|
|
A304708
|
|
Number of partitions (d1,d2,...,dm) of n such that d1/1 > d2/2 > ... > dm/m and d1 < d2 < ... < dm.
|
|
3
|
|
|
1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 3, 5, 5, 4, 5, 6, 6, 7, 8, 8, 9, 10, 12, 11, 13, 13, 16, 16, 15, 18, 21, 22, 26, 25, 28, 31, 33, 33, 35, 39, 41, 46, 47, 50, 53, 59, 63, 68, 74, 77, 84, 90, 93, 98, 105, 111, 119, 129, 132, 138, 149, 157, 169, 178, 189, 201, 211, 227
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
n | Partition (d1,d2,...,dm) | (d1/1, d2/2, ... , dm/m)
--+-----------------------------+-------------------------
1 | (1) | (1)
2 | (2) | (2)
3 | (3) | (3)
4 | (4) | (4)
5 | (5) | (5)
| (2, 3) | (2, 3/2)
6 | (6) | (6)
7 | (7) | (7)
| (3, 4) | (3, 2)
8 | (8) | (8)
| (3, 5) | (3, 5/2)
9 | (9) | (9)
| (4, 5) | (4, 5/2)
| (2, 3, 4) | (2, 3/2, 4/3)
|
|
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+1, t+1))))
end:
a:= n-> b(n, n+1, 1$2):
|
|
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 + 1, t + 1]]]];
a[n_] := b[n, n + 1, 1, 1];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|