login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of partitions of n such that (number of distinct parts) = maximal multiplicity of the parts.
5

%I #6 Apr 04 2014 13:30:05

%S 0,1,1,1,2,3,3,4,6,5,11,12,15,21,26,30,41,52,56,82,99,118,144,189,221,

%T 279,327,405,491,600,699,860,1038,1230,1470,1754,2106,2487,2970,3489,

%U 4148,4883,5779,6763,8024,9284,11006,12780,15029,17452,20405,23660

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

%e a(8) counts these partitions: 8, 611, 422, 332, 3311, 32111.

%t z = 58; d[p_] := d[p] = Length[DeleteDuplicates[p]]; m[p_] := Max[Map[Length, Split[p]]]; Table[Count[IntegerPartitions[n], p_ /; d[p] == m[p]], {n, 0, z}]

%Y Cf. A239948, A239966.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Mar 30 2014