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 A238623 #4 Mar 08 2014 22:51:39
%S A238623 0,1,1,3,3,8,8,17,19,35,39,66,76,120,140,209,246,355,419,585,695,946,
%T A238623 1123,1498,1781,2335,2775,3583,4255,5428,6436,8118,9616,12013,14202,
%U A238623 17592,20763,25525,30069,36711,43165,52382,61468,74173,86878,104303,121925
%N A238623 Number of partitions of n such that neither floor(n/2) nor ceiling(n/2) is a part.
%F A238623 a(n) + A238622(n) = A000041(n).
%e A238623 a(7) counts these 8 partitions: 7, 61, 52, 511, 2221, 22111, 211111, 1111111.
%t A238623 z=40; g[n_] := g[n] = IntegerPartitions[n];
%t A238623 t1 = Table[Count[g[n], p_ /; Or[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238622 [or] *)
%t A238623 t2 = Table[Count[g[n], p_ /; Nor[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238623 [nor] *)
%t A238623 t3 = Table[Count[g[n], p_ /; Xnor[MemberQ[p, Floor[n/2]], MemberQ[p, Ceiling[n/2]]]], {n, z}] (* A238624 [xnor] *)
%Y A238623 Cf. A238622, A238624.
%K A238623 nonn,easy
%O A238623 1,4
%A A238623 _Clark Kimberling_, Mar 02 2014