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%I #4 Apr 26 2014 01:28:52
%S 0,0,0,0,1,1,2,3,4,4,7,7,10,12,15,17,23,26,32,38,45,53,65,73,87,101,
%T 120,138,160,184,211,249,285,324,373,419,487,561,633,715,808,922,1040,
%U 1188,1336,1500,1695,1897,2119,2405,2704,3032,3383,3761,4185,4691
%N Number of partitions p of n into distinct parts, not including ceiling(mean(p)).
%F a(n) + A241314(n) = A000009(n) for n >= 1.
%e a(10) counts these 7 partitions: 91, 82, 73, 721, 64, 631, 532.
%t z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241312 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241313 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241314 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241315 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241316 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, ] (* A241317 *)
%Y Cf. A241312, A241313, A241314, A241318, A000009.
%K nonn,easy
%O 0,7
%A _Clark Kimberling_, Apr 19 2014
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