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%I #7 Feb 21 2024 08:20:13
%S 1,-1,1,-1,0,1,1,-1,-1,1,1,0,-1,0,1,-1,1,1,-1,-1,1,-1,0,1,0,-1,0,1,1,
%T -1,-1,1,1,-1,-1,1,1,0,-1,0,1,0,-1,0,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,0,
%U 1,0,-1,0,1,0,-1,0,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,-1,1,1,-1,-1,1,1
%N Inverse of number triangle A106468.
%C A 'mixed' sequence array : rows alternate between the rows of the sequence array for the sequence 1,-1,-1,1,1,-1,-1,.. with g.f. (1-x)/(1+x^2) and the sequence array for the sequence 1,0,-1,0,-1,... with g.f. 1/(1+x^2). Column 2k has g.f. x^2k(1-x)/(1+x^2) column 2k+1 has g.f. x^(2k+1)/(1+x^2). Row sums are 1,0,0,0,1,0,0,0,1,.. with g.f. 1/(1-x^4).
%e Triangle begins:
%e 1;
%e -1, 1;
%e -1, 0, 1;
%e 1, -1, -1, 1;
%e 1, 0, -1, 0, 1;
%e -1, 1, 1, -1, -1, 1;
%e ...
%K sign,tabl
%O 0,1
%A _Paul Barry_, May 03 2005
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