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A362548
Number of partitions of n with at least three parts larger than 1.
1
0, 0, 0, 0, 0, 0, 1, 2, 5, 9, 16, 25, 40, 58, 85, 119, 166, 224, 303, 399, 526, 681, 880, 1122, 1430, 1801, 2266, 2827, 3521, 4354, 5378, 6601, 8092, 9870, 12020, 14576, 17652, 21294, 25653, 30804, 36937, 44162, 52732, 62798, 74690, 88627, 105028, 124201, 146696, 172924, 203600, 239292, 280912
OFFSET
0,8
COMMENTS
Both following comments are empirical observations:
1) also accumulant of A119907;
2) the characters of exactly these partitions do not occur in the decomposition of the count of parts 1<=k<=n into the characters of the symmetric group of n (Elders' Theorem).
3) the complement (partitions with no more than 2 parts >1) is counted by A033638.
LINKS
Eric Weisstein's World of Mathematics, Elder's Theorem
FORMULA
a(n) = A000041(n) - A033638(n).
MATHEMATICA
Table[PartitionsP[n]-(1 + Floor[n^2/4]), {n, 0, 30}];
Table[ Count[Partitions[n], pa_ /; Length[DeleteCases[pa, 1]] > 2] , {n, 0, 30}]
PROG
(Python)
from sympy import npartitions
def A362548(n): return npartitions(n)-1-(n**2>>2) # Chai Wah Wu, Apr 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Apr 24 2023
STATUS
approved