cp's OEIS Frontend

A362548 Number of partitions of n with at least three parts larger than 1.

%I A362548 #21 Apr 27 2023 16:35:20
%S A362548 0,0,0,0,0,0,1,2,5,9,16,25,40,58,85,119,166,224,303,399,526,681,880,
%T A362548 1122,1430,1801,2266,2827,3521,4354,5378,6601,8092,9870,12020,14576,
%U A362548 17652,21294,25653,30804,36937,44162,52732,62798,74690,88627,105028,124201,146696,172924,203600,239292,280912
%N A362548 Number of partitions of n with at least three parts larger than 1.
%C A362548 Both following comments are empirical observations:
%C A362548 1) also accumulant of A119907;
%C A362548 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 A362548 3) the complement (partitions with no more than 2 parts >1) is counted by A033638.
%H A362548 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EldersTheorem.html">Elder's Theorem</a>
%F A362548 a(n) = A000041(n) - A033638(n).
%t A362548 Table[PartitionsP[n]-(1 + Floor[n^2/4]),{n,0,30}];
%t A362548 Table[ Count[Partitions[n], pa_ /; Length[DeleteCases[pa, 1]] > 2] , {n,0,30}]
%o A362548 (Python)
%o A362548 from sympy import npartitions
%o A362548 def A362548(n): return npartitions(n)-1-(n**2>>2) # _Chai Wah Wu_, Apr 27 2023
%Y A362548 Cf. A000041, A033638, A119907.
%K A362548 nonn
%O A362548 0,8
%A A362548 _Wouter Meeussen_, Apr 24 2023