proposed

approved

editing

proposed

For n >=1, a(n) is also the number of partitions of n such that (least part) > (multiplicity of greatest part), as well as the number of partitions p of n such that min(p) < min(c(p)), where c = conjugate.

proposed

editing

editing

proposed

allocated for Clark KimberlingNumber of partitions of n such that (least part) < (multiplicity of greatest part).

0, 0, 1, 1, 1, 2, 3, 4, 5, 7, 9, 13, 16, 22, 27, 36, 44, 59, 71, 93, 114, 144, 176, 223, 268, 336, 407, 502, 605, 744, 891, 1088, 1301, 1574, 1879, 2265, 2687, 3224, 3822, 4557, 5384, 6399, 7535, 8921, 10481, 12354, 14481, 17022, 19888, 23307, 27178, 31745

0,6

For n >=1, a(n) is also the number of partitions of n such that (least part) > (multiplicity of greatest part).

a(n) = A240179(n) - A240180(n), for n >= 0.

a(6) counts these 3 partitions: 222, 2211, 111111.

z = 60; f[n_] := f[n] = IntegerPartitions[n]; Table[Count[f[n], p_ /; Min[p] < Count[p, Max[p]]], {n, 0, z}] (* A240178 *)

Table[Count[f[n], p_ /; Min[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240179 *)

Table[Count[f[n], p_ /; Min[p] == Count[p, Max[p]]], {n, 0, z}] (* A240180 *)

Table[Count[f[n], p_ /; Min[p] > Count[p, Max[p]]], {n, 0, z}] (* A240178, n>0 *)

Table[Count[f[n], p_ /; Min[p] >= Count[p, Max[p]]], {n, 0, z}] (* A240179, n>0 *)

Cf. A240179, A240180.

allocated

nonn,easy

Clark Kimberling, Apr 02 2014

approved

editing

allocated for Clark Kimberling

allocated

approved