OFFSET
1,4
COMMENTS
Also, clearly, a(n) = number of partitions p of n such that m(p) > m(c(p)).
EXAMPLE
a(7) counts these 6 partitions: 7, 61, 52, 511, 43, 421, of which the respective conjugates are 1111111, 211111, 22111, 31111, 2221, 321.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 11 2014
STATUS
approved