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%I #12 May 30 2024 06:59:54
%S 0,0,1,1,2,5,6,11,18,27,36,61,77,115,161,223,291,416,531,729,951,1256,
%T 1605,2132,2694,3491,4423,5659,7079,9027,11201,14102,17484,21789,
%U 26822,33309,40734,50160,61195,74893,90846,110722,133697,162026,195104,235244
%N a(n) = sum for all integer partitions of n of the difference between number of different parts and number of different multiplicities.
%C Sum of the rows of A373241 or A373242.
%e From the eighth row of A373241: a(8)=11
%e 0, 1, 1, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0
%e or the tenth row of A373242: a(10)=27
%e 0, 4, 8, 8, 5, 1, 1, 0, 0, 0
%t Table[Plus @@
%t Table[Plus @@
%t Map[Length[Union[#]] - Length[Union[Length /@ Split[#]]] &,
%t IntegerPartitions[n, {k}]], {k, 1, n}], {n, 1, 40}]
%Y Cf. A373241, A373242.
%K nonn
%O 1,5
%A _Olivier Gérard_, May 29 2024