|
%I #11 Sep 28 2023 16:45:29
%S 0,2,2,2,2,4,4,8,10,10,14,18,18,26,30,36,44,60,64,82,96,114,130,164,
%T 176,222,248,296,338,406,450,550,620,726,816,968,1074,1270,1418,1648,
%U 1836,2150,2382,2758,3080,3534,3942,4538,5034,5778,6416,7312,8136,9258
%N Number of partitions p of n that are disjoint from their conjugate.
%C First column of the array at A240181.
%F a(n) = 2*A114701(n), for n >= 1.
%e a(6) counts these 4 partitions: 6, 33, 222, 111111, of which the respective conjugates are 111111, 222, 33, 6.
%t z = 30; p[n_, k_] := p[n, k] = IntegerPartitions[n][[k]]; c[p_] := c[p] = Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p]; b[n_] := b[n] = Table[Intersection[p[n, k], c[p[n, k]]], {k, 1, PartitionsP[n]}]; Table[Count[Map[Length, b[n]], 0], {n, 1, z}] (* this sequence *)
%t Table[Count[Map[Length, b[n]], 1], {n, 1, z}] (* A240675 *)
%Y Cf. A240675, A114701, A240181.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Apr 12 2014
%E Name corrected by _Clark Kimberling_, Sep 28 2023
|
