This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A238624 #4 Mar 08 2014 22:52:00
%S A238624 0,2,2,5,4,11,9,22,20,42,40,77,77,135,141,231,247,385,420,627,696,
%T A238624 1002,1124,1575,1782,2436,2776,3718,4256,5604,6437,8349,9617,12310,
%U A238624 14203,17977,20764,26015,30070,37338,43166,53174,61469,75175,86879,105558,121926
%N A238624 Number of partitions of n such that either both floor(n/2) and ceiling(n/2) are parts or else neither is a part.
%e A238624 a(7) counts these 9 partitions: 7, 61, 52, 511, 43, 2221, 22111, 211111, 1111111.
%t A238624 z=40; g[n_] := g[n] = IntegerPartitions[n];
%t A238624 t1 = Table[Count[g[n], p_ /; Or[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238622 [or] *)
%t A238624 t2 = Table[Count[g[n], p_ /; Nor[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238623 [nor] *)
%t A238624 t3 = Table[Count[g[n], p_ /; Xnor[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238624 [xnor] *)
%Y A238624 Cf. A238622, A238623.
%K A238624 nonn,easy
%O A238624 1,2
%A A238624 _Clark Kimberling_, Mar 02 2014