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 A115199 #4 Mar 14 2015 13:11:04 %S A115199 0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,1,0, %T A115199 0,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0,1, %U A115199 1,1,1,0,0,0,0,0,0,0,1,1,1 %N A115199 Parity of partitions of n, with 0 for even, 1 for odd. The definition follows. %C A115199 The main array with 0 and 1 interchanged is A115198. %C A115199 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. %C A115199 The row length sequence of this triangle is p(n)=A000041(n) (number of partitions). %C A115199 See the W. Lang link under A115198 for the first 10 rows where 0 and 1 should be swapped for this a(n,m) entry. %F A115199 a(n,m)= 0 if sum(e(n,m,2*j),j=1..floor(n/2)) is even, else 1, 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)=0. %e A115199 [0];[1,0];[0,1,0];[1,0,0,1,0];[0,1,1,0,0,1,0];... %e A115199 a(5,4)=0 because the 4th partition of n=5, (1^1,2^2)=(1,2,2), in the A-St order, has an even number of even parts (the number of even parts is in fact 2). %K A115199 nonn,easy,tabf %O A115199 0,1 %A A115199 _Wolfdieter Lang_, Feb 23 2006