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

1,5

Comments

Sum of the rows of A373241 or A373242.

Links

Table of n, a(n) for n=1..46.

Example

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

Mathematica

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

Crossrefs

Cf. A373241, A373242.

Sequence in context: A049054 A319140 A336902 * A135476 A255310 A051217

Adjacent sequences: A373240 A373241 A373242 * A373244 A373245 A373246

Keyword

nonn

Author

Olivier Gérard, May 29 2024

Status

approved