A240728 Number of partitions p of n such that m(p) = m(c(p)), where m = maximal multiplicity of parts, and c = conjugate.

1, 0, 1, 1, 1, 1, 3, 4, 4, 6, 6, 13, 13, 19, 20, 27, 35, 53, 52, 73, 86, 110, 123, 183, 194, 258, 286, 384, 423, 554, 624, 817, 915, 1144, 1305, 1651, 1865, 2301, 2633, 3252, 3709, 4538, 5163, 6263, 7194, 8604, 9848, 11795, 13507, 16086

Offset

1,7

Links

Table of n, a(n) for n=1..50.

Formula

a(n) + A240726(n) = A240727(n) for n >= 1.

a(n) + 2*A240726(n) = A000041(n) for n >= 1.

Example

a(7) counts these 3 partitions:  4111, 331, 322, of which the respective conjugates are 4111, 322, 331.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; c[p_] := Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p];  m[p_] := Max[Map[Length, Split[p]]];
Table[Count[f[n], p_ /; m[p] < m[c[p]]], {n, 1, z}]  (* A240726 *)
Table[Count[f[n], p_ /; m[p] <= m[c[p]]], {n, 1, z}] (* A240727 *)
Table[Count[f[n], p_ /; m[p] == m[c[p]]], {n, 1, z}] (* A240728 *)

Crossrefs

Cf. A240726, A240727, A240729, A000041.

Sequence in context: A088847 A120613 A277193 * A164326 A317645 A117571

Adjacent sequences: A240725 A240726 A240727 * A240729 A240730 A240731

Keyword

nonn,easy

Author

Clark Kimberling, Apr 11 2014

Status

approved