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%I #6 Mar 08 2014 22:51:29
%S 1,1,2,2,4,3,7,5,11,7,17,11,25,15,36,22,51,30,71,42,97,56,132,77,177,
%T 101,235,135,310,176,406,231,527,297,681,385,874,490,1116,627,1418,
%U 792,1793,1002,2256,1255,2829,1575,3532,1958,4393,2436,5445,3010,6727
%N Number of partitions of n such that floor(n/2) or ceiling(n/2) is a part.
%F a(n) + A238623(n) = A000041(n).
%e a(7) counts these partitions: 43, 421, 4111, 331, 322, 3211, 31111.
%t z=40; g[n_] := g[n] = IntegerPartitions[n];
%t t1 = Table[Count[g[n], p_ /; Or[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238622 [or] *)
%t t2 = Table[Count[g[n], p_ /; Nor[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238623 [nor] *)
%t t3 = Table[Count[g[n], p_ /; Xnor[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238624 [xnor] *)
%Y Cf. A238623, A238624.
%K nonn,easy
%O 1,3
%A _Clark Kimberling_, Mar 02 2014
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