|
|
A240851
|
|
Number of partitions p of n into distinct parts not including mean(p).
|
|
10
|
|
|
0, 0, 0, 1, 1, 2, 2, 4, 5, 5, 9, 11, 10, 17, 21, 21, 27, 37, 40, 53, 50, 69, 88, 103, 98, 126, 164, 183, 199, 255, 238, 339, 359, 437, 511, 510, 565, 759, 863, 969, 950, 1259, 1224, 1609, 1750, 1866, 2303, 2589, 2497, 3061, 3412, 4080, 4485, 5119, 5168, 6031
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(9) counts these 5 partitions: 81, 72, 63. 621, 54.
|
|
MATHEMATICA
|
z = 70; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; MemberQ[p, Mean[p]]], {n, 0, z}] (* A240850 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Mean[p]]], {n, 0, z}] (* A240851 *)
|
|
PROG
|
(Python)
from sympy.utilities.iterables import partitions
def A240851(n): return sum(1 for s, p in partitions(n, size=True) if max(p.values(), default=0)==1 and (n%s or n//s not in p)) # Chai Wah Wu, Sep 21 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|