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%I #12 Apr 26 2014 21:05:38
%S 1,0,0,0,1,1,3,3,6,8,11,12,27,23,33,51,68,67,114,111,186,217,242,277,
%T 502,501,571,760,1014,1021,1649,1549,2195,2506,2777,3712,5275,4919,
%U 5800,7259,10389,9858,13987,13846,18261,23029,23314,26523,40250,39613,49286
%N Number of partitions p of n such that neither floor(mean(p)) nor ceiling(mean(p)) is a part.
%e a(6) counts these 3 partitions: 51, 42, 411.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n];
%t t1 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241340 *)
%t t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241341 *)
%t t3 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241342 *)
%t t4 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241343 *)
%t t5 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241344 *)
%Y Cf. A241340, A241341, A241342, A241344.
%K nonn,easy
%O 0,7
%A _Clark Kimberling_, Apr 20 2014