A237870 Number of partitions of n such that (greatest part) + (least part) > number of parts.

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

Links

Table of n, a(n) for n=1..48.

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

Cf. A237822, A237823, A237869, A237871.

Sequence in context: A325092 A247186 A051061 * A191015 A181385 A188381

Adjacent sequences: A237867 A237868 A237869 * A237871 A237872 A237873

Keyword

nonn,easy

Author

Clark Kimberling, Feb 18 2014

Status

approved