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%I #6 Feb 22 2014 18:49:42
%S 0,1,0,1,1,1,1,4,2,4,5,7,8,13,12,18,22,30,33,46,51,69,81,102,120,155,
%T 179,224,265,326,383,476,553,674,793,956,1123,1353,1578,1886,2209,
%U 2624,3063,3630,4222,4979,5797,6803,7900,9256,10717,12507,14477,16836
%N Number of partitions of n such that (greatest part) + (least part) = number of parts.
%e a(8) = 4 counts these partitions: 3311, 3221, 2222, 41111.
%t z = 60; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := t[p] = Length[p];
%t Table[Count[q[n], p_ /; Max[p] + Min[p] < t[p]], {n, z}] (* A237822 *)
%t Table[Count[q[n], p_ /; Max[p] + Min[p] <= t[p]], {n, z}] (* A237823 *)
%t Table[Count[q[n], p_ /; Max[p] + Min[p] == t[p]], {n, z}] (* A237869 *)
%t Table[Count[q[n], p_ /; Max[p] + Min[p] > t[p]], {n, z}] (* A237870 *)
%t Table[Count[q[n], p_ /; Max[p] + Min[p] >= t[p]], {n, z}] (* A237871 *)
%Y Cf. A237822, A237823, A237870, A237871.
%K nonn,easy
%O 1,8
%A _Clark Kimberling_, Feb 18 2014
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