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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

Table of n, a(n) for n=0..70.

FORMULA

a(n) <= A304707(n).

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):

seq(a(n), n=0..80);  # Alois P. Heinz, May 17 2018

CROSSREFS

Cf. A053251, A053282, A304705, A304706, A304707.

Sequence in context: A185315 A232548 A029363 * A319688 A033922 A008624

Adjacent sequences:  A304705 A304706 A304707 * A304709 A304710 A304711

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 17 2018

STATUS

approved

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)