A373272 -id:A373272 - cp's OEIS frontend

A373273 a(n) = sum of all distinct multiplicities in every integer partition of n.

1, 3, 5, 11, 18, 29, 48, 74, 107, 161, 237, 324, 471, 648, 876, 1199, 1632, 2141, 2881, 3754, 4910, 6389, 8301, 10570, 13603, 17280, 21915, 27614, 34842, 43416, 54415, 67509, 83782, 103459, 127685, 156457, 192155, 234540, 286112, 347571, 422245, 510311, 617216

Offset: 1

Olivier Gérard, May 29 2024

nonn

Sum of the rows of triangle A373272.

Cf. A006128, A373272.

Table[Plus @@
  Map[Plus @@ Union[Length /@ Split[#]] &, IntegerPartitions[n]], {n,
  1, 40}]

A373104 Sum of all distinct multiplicities in the partitions of 2n into n parts.

Original entry on oeis.org

0, 1, 3, 7, 16, 28, 54, 90, 151, 235, 366, 554, 818, 1191, 1707, 2395, 3363, 4638, 6329, 8585, 11526, 15338, 20348, 26750, 34946, 45414, 58751, 75503, 96713, 123252, 156356, 197683, 248934, 312197, 390456, 486471, 604181, 748284, 924026, 1137591, 1397085

Offset: 0

Alois P. Heinz, Jun 01 2024

nonn

			a(4) = 16 = 4 + (1+2) + 2 + (1+2) + (1+3): 2222, 3221, 3311, 4211, 5111.

Cf. A373272.

a(n) = A373272(2n,n).

cp's OEIS Frontend

A373273 a(n) = sum of all distinct multiplicities in every integer partition of n.

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A373104 Sum of all distinct multiplicities in the partitions of 2n into n parts.

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