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%I #6 Feb 27 2014 20:22:47
%S 1,2,2,3,2,5,3,6,8,9,10,20,18,25,38,43,53,77,87,114,150,176,220,290,
%T 343,422,535,641,783,978,1164,1415,1733,2068,2497,3026,3595,4304,5174,
%U 6140,7300,8709,10283,12176,14435,16978,20001,23579,27640,32423,38024
%N Number of partitions p of n that include (min(p) + max(p))/2 as a part.
%C A238480(n) + A238481(n) = A000041(n).
%e a(6) counts these partitions:
%e 6 (as (6+6)/2 = 6 is included),
%e 33 (as (3+3)/2 = 3 is included),
%e 321 (as (3+1)/2 = 2 is included),
%e 222 (as (2+2)/2 = 2 is included),
%e 111111 (as (1+1)/2 = 1 is included).
%e Thus a(6) = 5.
%t Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, (Min[p] + Max[p])/2]], {n, 40}]
%Y Cf. A238481.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Feb 27 2014
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