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%I #3 Mar 30 2012 18:59:13
%S 1,1,1,0,2,0,1,1,1,1,0,1,2,1,0,0,1,1,1,1,0,0,0,1,3,1,0,0,1,0,1,1,1,1,
%T 0,1,0,1,0,1,3,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,1,1,3,1,1,1,0,0,0,0,
%U 1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,1,3,1,1,1,0,0,0,0,0,0,1,0,1,1,1,1,0,1,0,0,0
%N Correlation triangle for Fredholm-Rueppel sequence A036987.
%C Row sums are A115367. T(2n,n) is partial sums of squares of A036987(n).
%F G.f.: A(x)A(x*y)/(1-x^2*y) where A(x)=sum{k>=0, x^(2^k-1)}. Number triangle T(n, k)=sum{j=0..n, if(j<=k, A036987(k-j), 0)*if(j<=(n-k), A036987(n-k-j), 0)}
%e Triangle begins
%e 1,
%e 1, 1,
%e 0, 2, 0,
%e 1, 1, 1, 1,
%e 0, 1, 2, 1, 0,
%e 0, 1, 1, 1, 1, 0,
%e 0, 0, 1, 3, 1, 0, 0,
%e 1, 0, 1, 1, 1, 1, 0, 1,
%e 0, 1, 0, 1, 3, 1, 0, 1, 0,
%e 0, 1, 0, 1, 1, 1, 1, 0, 1, 0,
%e 0, 0, 1, 1, 1, 3, 1, 1, 1, 0, 0,
%e 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0,
%e 0, 0, 0, 1, 1, 1, 3, 1, 1, 1, 0, 0, 0,
%e 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0,
%e 0, 0, 0, 0, 1, 1, 1, 4, 1, 1, 1, 0, 0, 0, 0,
%e 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1,
%e 0, 1, 0, 0, 0, 1, 1, 1, 4, 1, 1, 1, 0, 0, 0, 1, 0
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Jan 21 2006
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