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%I
%S 1,0,1,0,-1,2,0,1,-2,3,0,0,0,-3,5,0,-1,2,0,-5,8,0,0,0,0,0,-8,13,0,1,
%T -2,3,0,0,-13,21,0,0,0,0,0,0,0,-21,34,0,0,0,-3,5,0,0,0,-34,55,0,0,0,0,
%U 0,0,0,0,0,-55,89,0,-1,2,0,-5,8,0,0,0
%N Inverse of the triangle A(n,k)=if(k<=n,if(n<=2k,1/F(n+1),0),0).
%C It is conjectured that all elements of this triangle are integers. Row sums are A127712.
%e Triangle begins
%e 1,
%e 0, 1,
%e 0, -1, 2,
%e 0, 1, -2, 3,
%e 0, 0, 0, -3, 5,
%e 0, -1, 2, 0, -5, 8,
%e 0, 0, 0, 0, 0, -8, 13,
%e 0, 1, -2, 3, 0, 0, -13, 21,
%e 0, 0, 0, 0, 0, 0, 0, -21, 34,
%e 0, 0, 0, -3, 5, 0, 0, 0, -34, 55,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, -55, 89,
%e 0, -1, 2, 0, -5, 8, 0, 0, 0, 0, -89, 144,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 233
%e Triangle is the inverse of the triangle
%e 1,
%e 0, 1,
%e 0, 1/2, 1/2,
%e 0, 0, 1/3, 1/3,
%e 0, 0, 1/5, 1/5, 1/5,
%e 0, 0, 0, 1/8, 1/8, 1/8,
%e 0, 0, 0, 1/13, 1/13, 1/13, 1/13,
%e 0, 0, 0, 0, 1/21, 1/21, 1/21, 1/21,
%e 0, 0, 0, 0, 1/34, 1/34, 1/34, 1/34, 1/34
%K sign,tabl
%O 0,6
%A _Paul Barry_, Jan 24 2007
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