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 A127711 Inverse of the triangle A(n,k)=if(k<=n,if(n<=2k,1/F(n+1),0),0). 2

%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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