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A304707 Number of partitions (d1,d2,...,dm) of n such that d1/1 >= d2/2 >= ... >= dm/m and d1 < d2 < ... < dm. 3
1, 1, 1, 2, 1, 2, 3, 2, 2, 4, 3, 4, 5, 4, 5, 7, 5, 7, 8, 8, 10, 12, 10, 11, 14, 14, 14, 18, 17, 20, 23, 22, 26, 30, 29, 32, 35, 34, 37, 43, 44, 48, 54, 54, 59, 67, 70, 76, 81, 84, 89, 97, 101, 110, 119, 123, 129, 139, 145, 155, 171, 176, 189, 201, 211, 228, 245, 257, 274, 295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..69.

EXAMPLE

n | Partition (d1,d2,...,dm)    | (d1/1, d2/2, ... , dm/m)

--+-----------------------------+-------------------------

1 | (1)                         | (1)

2 | (2)                         | (2)

3 | (3)                         | (3)

  | (1, 2)                      | (1, 1)

4 | (4)                         | (4)

5 | (5)                         | (5)

  | (2, 3)                      | (2, 3/2)

6 | (6)                         | (6)

  | (2, 4)                      | (2, 2)

  | (1, 2, 3)                   | (1, 1, 1)

7 | (7)                         | (7)

  | (3, 4)                      | (3, 2)

8 | (8)                         | (8)

  | (3, 5)                      | (3, 5/2)

9 | (9)                         | (9)

  | (3, 6)                      | (3, 3)

  | (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$2, 1$2):

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

CROSSREFS

Cf. A053251, A053282, A304705, A304706, A304708.

Sequence in context: A302257 A324748 A320387 * A112218 A172366 A132148

Adjacent sequences:  A304704 A304705 A304706 * A304708 A304709 A304710

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 17 2018

STATUS

approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)