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A373243
a(n) = sum for all integer partitions of n of the difference between number of different parts and number of different multiplicities.
3
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.
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
Sequence in context: A049054 A319140 A336902 * A135476 A255310 A051217
KEYWORD
nonn
AUTHOR
Olivier Gérard, May 29 2024
STATUS
approved