A336767 - OEIS

%I #10 Aug 06 2020 05:06:28

%S 1,-1,0,-1,1,-1,1,-1,1,-1,2,-1,2,-2,2,-3,2,-2,3,-3,3,-4,4,-4,4,-5,5,

%T -6,6,-6,7,-7,7,-8,9,-9,10,-10,11,-12,13,-13,14,-15,15,-17,18,-18,20,

%U -21,22,-23,24,-25,27,-29,30,-32,33,-35,37,-39,40,-43,45,-47,50

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

%H H. L. Alder and A. A. Muwafi, <a href="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 G.f.: Product_{n>0} ((1-q^(8*n))/(1+q^n)).

%Y Cf. A000041, A106459, A261775, A336766.

%K sign

%O 0,11

%A _Jeremy Lovejoy_, Aug 04 2020