login
A240182
Number of partitions of n such that (greatest part) <= (multiplicity of least part).
3
1, 1, 1, 1, 3, 2, 5, 4, 8, 10, 13, 15, 25, 25, 37, 46, 61, 70, 97, 112, 150, 177, 224, 270, 347, 407, 508, 611, 754, 895, 1106, 1304, 1594, 1892, 2283, 2708, 3262, 3835, 4595, 5421, 6452, 7574, 8993, 10530, 12445, 14564, 17123, 19992, 23465, 27302, 31931
OFFSET
0,5
FORMULA
a(n) = A240178(n) + A240183(n), for n >= 1.
a(n) + A240179(n) = A000041(n) for n >= 0.
EXAMPLE
a(8) counts these 8 partitions: 41111, 32111, 311111, 2222, 22211, 221111, 2111111, 11111111.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Max[p] < Count[p, Min[p]]], {n, 0, z}] (* A240178 except for n=0 *)
t2 = Table[Count[f[n], p_ /; Max[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240182 *)
t3 = Table[Count[f[n], p_ /; Max[p] == Count[p, Min[p]]], {n, 0, z}] (* A240183 *)
t4 = Table[Count[f[n], p_ /; Max[p] > Count[p, Min[p]]], {n, 0, z}] (* A240184 *)
t5 = Table[Count[f[n], p_ /; Max[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240179 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 02 2014
STATUS
approved