A376840 Take the integer partitions with at least 2 parts in order of their associated multinomial coefficients; a(n) is the sum of the n-th partition, i.e., the number of the row of A036038 (or A078760) in which the multinomial coefficient appears. In case of ties, take the sums (or row numbers) in nondecreasing order.

2, 3, 4, 5, 3, 4, 6, 7, 8, 9, 5, 10, 11, 4, 12, 13, 14, 6, 15, 16, 17, 18, 19, 5, 6, 20, 7, 21, 22, 23, 4, 24, 25, 26, 27, 8, 28, 29, 5, 6, 30, 31, 32, 33, 34, 7, 35, 9, 36, 37, 38, 39, 40, 41, 7, 42, 43, 44, 10, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 11, 55

Offset: 1

Author

Pontus von Brömssen, Oct 06 2024

Keywords

• nonn

Comments

Equivalently, a(n) is the number of the row of A036038 (or A078760) in which A376367(n) appears, with row numbers in nondecreasing order for numbers that appear multiple times in A376367.

The multinomial coefficient of the n-th partition, with the ordering considered here, is A376367(n).

Examples

			  n | A376367(n) | partition | a(n)
  --+------------+-----------+-----
  1 |     2      |  (1,1)    |  2
  2 |     3      |  (2,1)    |  3
  3 |     4      |  (3,1)    |  4
  4 |     5      |  (4,1)    |  5
  5 |     6      |  (1,1,1)  |  3
  6 |     6      |  (2,2)    |  4
  7 |     6      |  (5,1)    |  6
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..10000
• Pontus von Brömssen, Log-log plot, using Plot2.

Crossrefs

Cf. A036038, A056239, A078760, A376367, A376379.

Formula

a(n) = A056239(A376379(n)).