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Number of partitions of n having an integer median.
108

%I #17 Feb 22 2023 21:41:58

%S 1,2,2,5,5,10,11,21,23,37,45,69,83,118,145,203,250,334,415,546,673,

%T 868,1074,1369,1681,2113,2590,3230,3942,4867,5920,7265,8791,10713,

%U 12923,15664,18818,22685,27156,32595,38879,46452,55231,65741,77900,92383,109153

%N Number of partitions of n having an integer median.

%C This sequence and A307683 partition the partition numbers, A000041.

%H Fausto A. C. Cariboni, <a href="/A325347/b325347.txt">Table of n, a(n) for n = 1..180</a>

%e a(5) counts these 5 partitions: [5], [3,1,1], [2,2,1], [2,1,1,1], [1,1,1,1,1].

%t Table[Count[IntegerPartitions[n], q_ /; IntegerQ[Median[q]]], {n, 10}]

%Y Cf. A000041, A307683.

%K nonn

%O 1,2

%A _Clark Kimberling_, Apr 23 2019