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A304706 Number of partitions (d1,d2,...,dm) of n such that d1/1 > d2/2 > ... > dm/m and 0 < d1 <= d2 <= ... <= dm. 3
1, 1, 2, 2, 3, 3, 4, 3, 6, 5, 6, 6, 8, 7, 11, 10, 11, 12, 15, 14, 18, 17, 20, 23, 27, 25, 31, 32, 35, 38, 43, 43, 51, 54, 59, 63, 71, 73, 85, 89, 96, 102, 113, 120, 134, 141, 149, 161, 175, 183, 203, 213, 233, 252, 280, 293, 319, 338, 360, 383, 409, 430, 468, 493, 531, 565 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..65.

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

CROSSREFS

Cf. A053251, A053282, A304705, A304707, A304708.

Sequence in context: A110676 A117171 A325356 * A084054 A106747 A335979

Adjacent sequences:  A304703 A304704 A304705 * A304707 A304708 A304709

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 17 2018

STATUS

approved

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Last modified October 1 15:55 EDT 2020. Contains 337443 sequences. (Running on oeis4.)