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%I #5 Feb 22 2014 18:49:50
%S 1,1,2,3,4,7,9,12,18,24,32,44,57,75,100,129,165,213,272,345,437,549,
%T 688,861,1069,1324,1638,2017,2474,3031,3698,4500,5468,6622,8001,9649,
%U 11605,13931,16694,19959,23815,28372,33734,40041,47454,56139,66309,78210
%N Number of partitions of n such that (greatest part) + (least part) > number of parts.
%e a(5) = 4 counts these partitions: 5, 41, 32, 311.
%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, A237869, A237871.
%K nonn,easy
%O 1,3
%A _Clark Kimberling_, Feb 18 2014
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