

A240178


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


7



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
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OFFSET

0,6


COMMENTS

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.


LINKS

Table of n, a(n) for n=0..51.


FORMULA

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


EXAMPLE

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


MATHEMATICA

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 *)


CROSSREFS

Cf. A240179, A240180.
Sequence in context: A250553 A026450 A280451 * A039863 A036802 A333265
Adjacent sequences: A240175 A240176 A240177 * A240179 A240180 A240181


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Apr 02 2014


STATUS

approved



