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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
a(n) + A240850(n) = A000009(n) for n >= 0.
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
Sequence in context: A349464 A325260 A325325 * A261665 A208096 A049269
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2014
STATUS
approved

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)