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A239959 Number of partitions of n such that 2*(number of distinct parts) = number of parts.

%I A239959 #7 Mar 19 2023 15:09:30
%S A239959 1,0,1,0,1,1,3,2,3,3,8,8,11,14,19,19,29,37,47,61,79,85,114,141,168,
%T A239959 210,257,309,395,468,556,685,816,966,1162,1380,1667,1988,2340,2777,
%U A239959 3305,3900,4571,5423,6348,7385,8700,10188,11846,13876,16118,18757,21846
%N A239959 Number of partitions of n such that 2*(number of distinct parts) =  number of parts.
%H A239959 Alois P. Heinz, <a href="/A239959/b239959.txt">Table of n, a(n) for n = 0..1000</a>
%e A239959 a(10) counts these 8 partitions:  7111, 55, 4411, 4222, 421111, 3331, 3322, 322111.
%p A239959 b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
%p A239959      `if`(i<1, 0, add(b(n-i*j, i-1, t+`if`(j>0, 2, 0)-j), j=0..n/i)))
%p A239959     end:
%p A239959 a:= n-> b(n$2, 0):
%p A239959 seq(a(n), n=0..60);
%t A239959 z = 55; d[p_] := d[p] = Length[DeleteDuplicates[p]]; Table[Count[IntegerPartitions[n], p_ /; 2*d[p] == Length[p]], {n, 0, z}]
%Y A239959 Cf. A239954.
%K A239959 nonn,easy
%O A239959 0,7
%A A239959 _Clark Kimberling_, Mar 30 2014