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A237823
Number of partitions of n such that (greatest part) + (least part) <= number of parts.
5
0, 1, 1, 2, 3, 4, 6, 10, 12, 18, 24, 33, 44, 60, 76, 102, 132, 172, 218, 282, 355, 453, 567, 714, 889, 1112, 1372, 1701, 2091, 2573, 3144, 3849, 4675, 5688, 6882, 8328, 10032, 12084, 14491, 17379, 20768, 24802, 29527, 35134, 41680, 49419, 58445, 69063, 81426
OFFSET
1,4
EXAMPLE
a(6) = 4 counts these partitions: 3111, 2211, 21111, 111111.
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