login
A240304
Number of partitions of n such that (maximal multiplicity of parts) > (multiplicity of the least part).
2
0, 0, 0, 0, 0, 1, 0, 2, 3, 4, 5, 12, 11, 21, 27, 37, 49, 71, 87, 124, 153, 204, 260, 344, 421, 550, 685, 867, 1076, 1360, 1660, 2081, 2544, 3145, 3831, 4706, 5692, 6958, 8395, 10171, 12224, 14761, 17645, 21204, 25281, 30207, 35914, 42760, 50618, 60057, 70914
OFFSET
0,8
FORMULA
a(n) + A240303(n) = A000041(n) for n >= 1.
EXAMPLE
a(7) counts these 2 partitions of 7: 331, 2221.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n]; m[p_] := Max[Map[Length, Split[p]]] (* maximal multiplicity *)
Table[Count[f[n], p_ /; m[p] == Count[p, Min[p]]], {n, 0, z}] (* A240303 *)
Table[Count[f[n], p_ /; m[p] > Count[p, Min[p]]], {n, 0, z}] (* A240304 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 04 2014
STATUS
approved