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A241090 Number of partitions p of n such that (number of numbers in p having multiplicity > 1) = number of 1s in p. 3

%I

%S 1,0,1,1,1,3,3,5,6,10,12,16,21,29,36,47,58,77,93,121,146,185,225,280,

%T 338,419,505,612,743,888,1075,1283,1539,1822,2190,2575,3073,3612,4287,

%U 5022,5936,6938,8158,9527,11151,12983,15156,17617,20468,23770,27531

%N Number of partitions p of n such that (number of numbers in p having multiplicity > 1) = number of 1s in p.

%e a(6) counts these 3 partitions: 6, 42, 2211.

%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; Table[Count[f[n], p_ /; e[p] == Count[p, 1]], {n, 0, z}]

%Y Cf. A241409, A241131.

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Apr 24 2014

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Last modified October 23 12:42 EDT 2021. Contains 348214 sequences. (Running on oeis4.)