A362548 - OEIS

%I #21 Apr 27 2023 16:35:20

%S 0,0,0,0,0,0,1,2,5,9,16,25,40,58,85,119,166,224,303,399,526,681,880,

%T 1122,1430,1801,2266,2827,3521,4354,5378,6601,8092,9870,12020,14576,

%U 17652,21294,25653,30804,36937,44162,52732,62798,74690,88627,105028,124201,146696,172924,203600,239292,280912

%N Number of partitions of n with at least three parts larger than 1.

%C Both following comments are empirical observations:

%C 1) also accumulant of A119907;

%C 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).

%C 3) the complement (partitions with no more than 2 parts >1) is counted by A033638.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EldersTheorem.html">Elder's Theorem</a>

%F a(n) = A000041(n) - A033638(n).

%t Table[PartitionsP[n]-(1 + Floor[n^2/4]),{n,0,30}];

%t Table[ Count[Partitions[n], pa_ /; Length[DeleteCases[pa, 1]] > 2] , {n,0,30}]

%o (Python)

%o from sympy import npartitions

%o def A362548(n): return npartitions(n)-1-(n**2>>2) # _Chai Wah Wu_, Apr 27 2023

%Y Cf. A000041, A033638, A119907.

%K nonn

%O 0,8

%A _Wouter Meeussen_, Apr 24 2023