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

1,1

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).

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Pontus von Brömssen, Log-log plot, using Plot2.

Formula

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

Example

  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

Crossrefs

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

Sequence in context: A215092 A345018 A382926 * A377488 A309079 A194551

Adjacent sequences: A376837 A376838 A376839 * A376841 A376842 A376843

Keyword

nonn

Author

Pontus von Brömssen, Oct 06 2024

Status

approved