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%I #7 Apr 26 2014 21:08:52
%S 0,1,2,3,4,5,7,8,11,15,18,22,37,36,50,73,89,100,152,161,249,290,330,
%T 413,646,666,803,1060,1348,1473,2170,2183,3003,3455,3984,5318,6936,
%U 6839,8494,10664,14064,14322,19343,20418,26417,32021,34068,40921,56205,57543
%N Number of partitions p of n such that floor(mean(p)) and ceiling(mean(p)) are parts of p.
%F a(n) + A241344(n) = A000041(n) for n >=1.
%e a(6) counts these 8 partitions: 6, 33, 321, 3111, 222, 2211, 21111, 111111.
%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. A241341, A241342, A241343, A241344.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Apr 20 2014
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