A240182 Number of partitions of n such that (greatest part) <= (multiplicity of least part).

1, 1, 1, 1, 3, 2, 5, 4, 8, 10, 13, 15, 25, 25, 37, 46, 61, 70, 97, 112, 150, 177, 224, 270, 347, 407, 508, 611, 754, 895, 1106, 1304, 1594, 1892, 2283, 2708, 3262, 3835, 4595, 5421, 6452, 7574, 8993, 10530, 12445, 14564, 17123, 19992, 23465, 27302, 31931

Offset

0,5

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = A240178(n) + A240183(n), for n >= 1.

a(n) + A240179(n) = A000041(n) for n >= 0.

Example

a(8) counts these 8 partitions:  41111, 32111, 311111, 2222, 22211, 221111, 2111111, 11111111.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Max[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240178 except for n=0 *)
t2 = Table[Count[f[n], p_ /; Max[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240182 *)
t3 = Table[Count[f[n], p_ /; Max[p] == Count[p, Min[p]]], {n, 0, z}] (* A240183 *)
t4 = Table[Count[f[n], p_ /; Max[p] > Count[p, Min[p]]], {n, 0, z}] (* A240184 *)
t5 = Table[Count[f[n], p_ /; Max[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240179 *)

Crossrefs

Cf. A240178, A240183, A240184, A240179, A000041.

Sequence in context: A240729 A339371 A258259 * A364311 A115297 A275900

Adjacent sequences: A240179 A240180 A240181 * A240183 A240184 A240185

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2014

Status

approved