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%I #6 Apr 26 2014 21:24:46
%S 1,0,0,0,1,2,4,6,10,14,20,28,38,52,69,89,119,156,195,256,320,408,520,
%T 646,792,1021,1249,1528,1889,2341,2810,3510,4204,5130,6230,7445,8925,
%U 11050,13044,15446,18486,22421,26288,31616,36986,43991,52574,61425,71449
%N Number of partitions p of n not including ceiling(mean(p)) as a part.
%e a(6) counts these 4 partitions: 51, 42, 411, 3111.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241334 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241335 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241336 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241337 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241338 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241339 *)
%Y Cf. A241334, A241335, A241336, A000041, A241312.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 20 2014
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