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A304705 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, 3, 3, 4, 6, 5, 6, 8, 9, 9, 12, 11, 14, 17, 16, 17, 23, 22, 27, 31, 30, 33, 40, 41, 46, 50, 54, 57, 70, 70, 77, 88, 92, 99, 111, 115, 129, 142, 152, 160, 175, 183, 199, 223, 234, 255, 283, 299, 328, 347, 370, 390, 430, 455, 489, 523, 557, 592, 642, 674, 724, 784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

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, 2)                      | (1, 1)

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

  | (1, 1, 1, 1, 1)             | (1, 1/2, 1/3, 1/4, 1/5)

6 | (6)                         | (6)

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

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

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

  | (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)

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

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

  | (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)

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

  | (4, 5)                      | (4, 5/2)

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

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

  | (1, 2, 3, 3)                | (1, 1, 1, 3/4)

  | (1, 2, 2, 2, 2)             | (1, 1, 2/3, 1/2, 2/5)

  | (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$2, 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];

a /@ Range[0, 80] (* Jean-François Alcover, Nov 23 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A053251, A053282, A304706, A304707, A304708.

Sequence in context: A200251 A207100 A281365 * A131187 A099072 A257241

Adjacent sequences:  A304702 A304703 A304704 * A304706 A304707 A304708

KEYWORD

nonn,changed

AUTHOR

Seiichi Manyama, May 17 2018

STATUS

approved

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Last modified November 28 03:13 EST 2020. Contains 338699 sequences. (Running on oeis4.)