%I A115199
%S A115199 0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,
%T A115199 0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0,1,1,1,
%U A115199 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 4-th 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).
%Y A115199 Sequence in context: A164349 A094186 A003849 this_sequence A085242 A059620 
               A083651
%Y A115199 Adjacent sequences: A115196 A115197 A115198 this_sequence A115200 A115201 
               A115202
%K A115199 nonn,easy,tabf
%O A115199 0,1
%A A115199 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 23 
               2006