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Number of partitions of n such that (number of distinct parts) = minimal multiplicity of the parts.
1

%I #4 Apr 04 2014 13:30:15

%S 0,1,1,1,1,1,2,2,4,3,6,5,8,6,13,6,15,10,19,12,24,15,33,22,38,28,52,39,

%T 61,51,78,66,94,85,118,103,140,130,168,165,194,190,244,230,274,285,

%U 328,327,394,386,449,485,522,540,646,639,712,790,846,880,1025

%N Number of partitions of n such that (number of distinct parts) = minimal multiplicity of the parts.

%e a(8) counts these 4 partitions : 8, 3311, 22211, 221111.

%t z = 61; d[p_] := d[p] = Length[DeleteDuplicates[p]]; m[p_] := Min[Map[Length, Split[p]]]; Table[Count[IntegerPartitions[n], p_ /; d[p] == m[p]], {n, 0, z}]

%Y Cf. A239964, A239948.

%K nonn,easy

%O 0,7

%A _Clark Kimberling_, Mar 30 2014