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%I #2 Mar 30 2012 18:59:19
%S 1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,1,0,0,
%T 1,1,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,0,1,
%U 1,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0
%N Triangle whose row sums modulo 2 give the Fredholm-Rueppel sequence A036987.
%C Row sums are A111982. Unsigned version of A111967.
%F G.f. of k-th column is x^k*if(k=0,1,x*sum{j=0..\infty, x^(-2^(j/2)*(((k+2)/(2*sqrt(2))-(k+1))(-1)^j-(k+2)/(2*sqrt(2))-(k+1))-(k+2))+1+x}
%e Triangle begins
%e 1,
%e 0, 1,
%e 0, 1, 1,
%e 0, 1, 1, 1,
%e 0, 0, 0, 1, 1,
%e 0, 1, 1, 0, 1, 1,
%e 0, 0, 0, 0, 0, 1, 1,
%e 0, 1, 1, 1, 0, 0, 1, 1,
%e 0, 0, 0, 0, 0, 0, 0, 1, 1,
%e 0, 0, 0, 1, 1, 0, 0, 0, 1, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
%e 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1
%K easy,nonn,tabl
%O 0,1
%A _Paul Barry_, Jan 30 2007