A240730 Number of partitions p of n such that m(p) <= m(c(p)), where m = minimal multiplicity of parts, and c = conjugate.

1, 1, 2, 4, 6, 8, 13, 17, 26, 34, 49, 64, 90, 116, 157, 205, 269, 341, 450, 566, 729, 913, 1164, 1447, 1831, 2255, 2822, 3470, 4307, 5254, 6485, 7875, 9646, 11669, 14209, 17107, 20731, 24848, 29956, 35801, 42949, 51116, 61098, 72484, 86268, 102035, 121001

Offset

1,3

Links

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

Formula

a(n) - A240729(n) = A240731(n) for n >= 1.

a(n) + A240729(n) = A000041(n) for n >= 1.

Example

a(7) counts all 15 partitions of 7 except 2111, 1111111, of which the respective conjugates are 52, 7.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; c[p_] := Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p];  m[p_] := Min[Map[Length, Split[p]]];
Table[Count[f[n], p_ /; m[p] < m[c[p]]], {n, 1, z}] (* A240729 *)
Table[Count[f[n], p_ /; m[p] <= m[c[p]]], {n, 1, z}] (* A240730 *)
Table[Count[f[n], p_ /; m[p] == m[c[p]]], {n, 1, z}] (* A240731 *)

Crossrefs

Cf. A240727, A240729, A240731, A000041.

Sequence in context: A135109 A281615 A213506 * A039846 A367218 A094092

Adjacent sequences: A240727 A240728 A240729 * A240731 A240732 A240733

Keyword

nonn,easy

Author

Clark Kimberling, Apr 11 2014

Status

approved