cp's OEIS Frontend

A336766 The number of partitions of n into an even number of parts, each part occurring at most five times, minus the number of partitions of n into an odd number of parts, each part occurring at most five times.

%I A336766 #16 Jan 05 2025 19:51:41
%S A336766 1,-1,0,-1,1,-1,0,0,2,-1,1,-1,1,-1,1,-1,2,-2,1,-2,2,-2,1,-2,3,-3,2,-2,
%T A336766 3,-3,3,-3,4,-4,3,-4,5,-4,4,-4,6,-5,5,-6,6,-7,6,-6,8,-8,7,-8,9,-9,8,
%U A336766 -9,11,-11,10,-11,12,-12,11,-13,15,-15,14,-15,17,-17,16,-17
%N A336766 The number of partitions of n into an even number of parts, each part occurring at most five times, minus the number of partitions of n into an odd number of parts, each part occurring at most five times.
%H A336766 H. L. Alder and A. A. Muwafi, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/13-2/alder.pdf">Identities relating the number of partitions into an even and odd number of parts</a>, Fibonacci Quarterly, 13 (1975), 147-149.
%F A336766 G.f.: Product_{n>0} ((1-q^(6*n))/(1+q^n)).
%e A336766 There are 10 partitions of 6 where parts occur at most five times: 6, 5+1, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, and so a(6) = 0.
%Y A336766 Cf. A000041, A106459, A219601, A336767.
%K A336766 sign
%O A336766 0,9
%A A336766 _Jeremy Lovejoy_, Aug 04 2020