A373243 a(n) = sum for all integer partitions of n of the difference between number of different parts and number of different multiplicities.

0, 0, 1, 1, 2, 5, 6, 11, 18, 27, 36, 61, 77, 115, 161, 223, 291, 416, 531, 729, 951, 1256, 1605, 2132, 2694, 3491, 4423, 5659, 7079, 9027, 11201, 14102, 17484, 21789, 26822, 33309, 40734, 50160, 61195, 74893, 90846, 110722, 133697, 162026, 195104, 235244

Offset: 1

Author

Olivier Gérard, May 29 2024

Keywords

• nonn

Comments

Sum of the rows of A373241 or A373242.

Examples

			From the eighth row of A373241: a(8)=11
  0, 1, 1, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0
or the tenth row of A373242: a(10)=27
  0, 4, 8, 8, 5, 1, 1, 0, 0, 0
		

Crossrefs

Cf. A373241, A373242.

Programs

Mathematica

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