This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115198 #14 Aug 29 2019 16:19:02 %S A115198 1,0,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1, %T A115198 1,1,1,0,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,1,1,0,1,1,0, %U A115198 0,0,0,1,1,1,1,1,1,1,0,0,0 %N A115198 Parity of partitions of n, with 1 for even, 0 for odd (!). The definition follows. %C A115198 The array with 0 and 1 interchanged is A115199. %C A115198 The partitions appear in the Abramowitz-Stegun (A-St) order (see the reference, pp. 831-2). %C A115198 A partition of n is (here) called even, resp. odd, if the number of even parts is even, resp. odd. A partition with no (0) even part is therefore even. Because the parity of permutations is linked, via their cycle structure, to the number of even parts of partitions one uses here 1 in order to mark the relevant (even) partitions. %C A115198 The row length sequence of this array is p(n)=A000041(n) (number of partitions). %H A115198 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. %H A115198 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972. %H A115198 W. Lang: <a href="/A115198/a115198.txt">First 10 rows.</a> %F A115198 a(n,m)= 1 if sum(e(n,m,2*j),j=1..floor(n/2)) is even, else 0, with the exponents e(n,m,k) of the m-th partition of n in the A-St order; i.e. the sum of the exponents of the even parts of the partition (1^e(n,m,1),2^e(n,m,2),..., n^e(n,m,n)) is even iff a(n,m)=1. %e A115198 [1];[0,1];[1,0,1];[0,1,1,0,1];[1,0,0,1,1,0,1];... %e A115198 a(4,4)=0 because it refers to the 4th partition of n=4 of the %e A115198 mentioned A-St ordering, namely to (1^2,2^1)=(1,1,2) which has an odd number %e A115198 (1) of even parts. %e A115198 a(5,4)=1 because (1^1,2^2)=(1,2,2) has an even number of even parts %e A115198 (the number of even parts is in fact 2). %Y A115198 The sequence of row lengths is A046682 (number of cycle types for even permutations). %K A115198 nonn,easy,tabf %O A115198 0,1 %A A115198 _Wolfdieter Lang_, Feb 23 2006