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%I #5 May 06 2014 15:04:20
%S 0,1,2,3,4,5,7,10,13,18,24,31,44,57,73,94,127,166,203,268,338,424,548,
%T 674,858,1046,1321,1643,1973,2472,3026,3774,4529,5455,6736,8013,9699,
%U 11899,14299,16926,20377,24373,29018,34679,41447,48688,57395,68775,81535
%N Number of partitions p of n such that round(mean(p)) is a part of p; here, round(x) means floor(x + 1/2).
%C For the corresponding sequence using "round" as in Mathematica, see A241338.
%F a(n) + A241734(n) = A000041(n) for n >= 0.
%e a(6) counts these 7 partitions: 6, 33, 321, 222, 2211, 21111, 111111.
%t z = 40; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p] + 1/2]]], {n, 0, z}] (* A241733 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p] + 1/2]]], {n, 0, z}] (* A241734 *)
%Y Cf. A241338, A241734.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Apr 28 2014
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