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

1,4

Links

Table of n, a(n) for n=1..47.

Example

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

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 *)

Crossrefs

Cf. A118084, A237757, A237799, A237800.

Sequence in context: A323595 A136460 A000065 * A023499 A103445 A001747

Adjacent sequences: A237755 A237756 A237757 * A237759 A237760 A237761

Keyword

nonn,easy

Author

Clark Kimberling, Feb 15 2014

Status

approved