A237758 Number of partitions of n such that 2*(least part) < number of parts.

0, 0, 1, 2, 4, 6, 10, 14, 21, 30, 42, 58, 80, 108, 144, 192, 252, 329, 426, 549, 702, 895, 1131, 1427, 1789, 2237, 2781, 3450, 4259, 5247, 6436, 7878, 9607, 11693, 14182, 17172, 20727, 24974, 30008, 35997, 43072, 51457, 61330, 72988, 86677, 102785, 121645

Offset: 1

Author

Clark Kimberling, Feb 15 2014

Keywords

• nonn
• easy

Examples

			a(5) = 4 counts these partitions: 311, 221, 2111, 11111.
		

Crossrefs

Cf. A118084, A237757, A237799, A237800.

Programs

Mathematica

z = 55; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := Length[p];
Table[Count[q[n], p_ /; 2 Min[p] < t[p]], {n, z}]   (* A237758 *)
Table[Count[q[n], p_ /; 2 Min[p] <= t[p]], {n, z}]  (* A118084 *)
Table[Count[q[n], p_ /; 2 Min[p] == t[p]], {n, z}]  (* A237757 *)
Table[Count[q[n], p_ /; 2 Min[p] > t[p]], {n, z}]   (* A237799 *)
Table[Count[q[n], p_ /; 2 Min[p] >= t[p]], {n, z}]  (* A237800 *)