A115381 - OEIS

%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