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 A238481 #11 Feb 27 2014 20:23:07
%S A238481 0,0,1,2,5,6,12,16,22,33,46,57,83,110,138,188,244,308,403,513,642,826,
%T A238481 1035,1285,1615,2014,2475,3077,3782,4626,5678,6934,8410,10242,12386,
%U A238481 14951,18042,21711,26011,31198,37283,44465,52978,62999,74699,88580,104753
%N A238481 Number of partitions p of n that do not include (min(p) + max(p))/2 as a part.
%F A238481 A238480(n) + A238481(n) = A000041(n).
%e A238481 a(6) counts these partitions:
%e A238481 51 (as part (5+1)/2 = 3 is not included),
%e A238481 42 (as (4+2)/2 = 3 is not included),
%e A238481 411 (as (4+1)/2 = 2.5 cannot be included),
%e A238481 3111 (as (3+1)/2 = 2 is not included),
%e A238481 2211 (as (2+1)/2 = 1.5 cannot be included),
%e A238481 21111 (ditto).
%e A238481 Thus a(6) = 6.
%t A238481 Table[Count[IntegerPartitions[n], p_ /; !MemberQ[p, (Min[p] + Max[p])/2]], {n, 40}]
%Y A238481 Cf. A238480.
%K A238481 nonn,easy
%O A238481 1,4
%A A238481 _Clark Kimberling_, Feb 27 2014