A240184 Number of partitions of n such that (greatest part) > (multiplicity of least part).

0, 0, 1, 2, 2, 5, 6, 11, 14, 20, 29, 41, 52, 76, 98, 130, 170, 227, 288, 378, 477, 615, 778, 985, 1228, 1551, 1928, 2399, 2964, 3670, 4498, 5538, 6755, 8251, 10027, 12175, 14715, 17802, 21420, 25764, 30886, 37009, 44181, 52731, 62730, 74570, 88435, 104762

Offset

0,4

Links

Table of n, a(n) for n=0..47.

Formula

A240178(n) + A240183(n) + a(n ) = A000041(n) for n >= 1.

Example

a(6) counts these 6 partitions:  6, 51, 42, 411, 33, 321.

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 *)
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, A240182, A240183, A240179, A000041.

Sequence in context: A348324 A007988 A241449 * A317853 A238517 A335240

Adjacent sequences: A240181 A240182 A240183 * A240185 A240186 A240187

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2014

Status

approved