|
|
A240206
|
|
Number of partitions p of n such that mean(p) > multiplicity(min(p)).
|
|
5
|
|
|
0, 0, 1, 2, 2, 4, 5, 9, 11, 16, 22, 31, 39, 56, 71, 91, 123, 157, 195, 263, 324, 405, 529, 649, 790, 1032, 1253, 1514, 1902, 2357, 2826, 3497, 4179, 5153, 6279, 7459, 8880, 11079, 13089, 15435, 18438, 22596, 26514, 31423, 36783, 44336, 52827, 61570, 71653
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(6) counts these 5 partitions: 6, 51, 42, 33, 321.
|
|
MATHEMATICA
|
z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Min[p]]], {n, 0, z}] (* A240203 *)
t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240204 *)
t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Min[p]]], {n, 0, z}] (* A240205 *)
t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Min[p]]], {n, 0, z}] (* A240206 *)
t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240079 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|