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A237870
Number of partitions of n such that (greatest part) + (least part) > number of parts.
5
1, 1, 2, 3, 4, 7, 9, 12, 18, 24, 32, 44, 57, 75, 100, 129, 165, 213, 272, 345, 437, 549, 688, 861, 1069, 1324, 1638, 2017, 2474, 3031, 3698, 4500, 5468, 6622, 8001, 9649, 11605, 13931, 16694, 19959, 23815, 28372, 33734, 40041, 47454, 56139, 66309, 78210
OFFSET
1,3
EXAMPLE
a(5) = 4 counts these partitions: 5, 41, 32, 311.
MATHEMATICA
z = 60; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := t[p] = Length[p];
Table[Count[q[n], p_ /; Max[p] + Min[p] < t[p]], {n, z}] (* A237822 *)
Table[Count[q[n], p_ /; Max[p] + Min[p] <= t[p]], {n, z}] (* A237823 *)
Table[Count[q[n], p_ /; Max[p] + Min[p] == t[p]], {n, z}] (* A237869 *)
Table[Count[q[n], p_ /; Max[p] + Min[p] > t[p]], {n, z}] (* A237870 *)
Table[Count[q[n], p_ /; Max[p] + Min[p] >= t[p]], {n, z}] (* A237871 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 18 2014
STATUS
approved