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Inverse of number triangle related to Fibonacci numbers.
1

%I #3 Mar 30 2012 18:59:09

%S 1,-1,1,-2,-2,1,0,-6,-3,1,0,0,-12,-4,1,0,0,0,-20,-5,1,0,0,0,0,-30,-6,

%T 1,0,0,0,0,0,-42,-7,1,0,0,0,0,0,0,-56,-8,1,0,0,0,0,0,0,0,-72,-9,1,0,0,

%U 0,0,0,0,0,0,-90,-10,1,0,0,0,0,0,0,0,0,0,-110,-11,1,0,0,0,0,0,0,0,0,0,0,-132,-12,1

%N Inverse of number triangle related to Fibonacci numbers.

%C Row sums are 1-n^2 with g.f. (1-3x)/(1-x)^3. Diagonal sums are A110315. Inverse of A039948.

%F T(n, k)=if(n=k, 1, if(n-k=1, -binomial(n, 1), if(n-k=2, -2*binomial(n, 2), 0)))

%e Rows begin

%e 1;

%e -1,1;

%e -2,-2,1;

%e 0,-6,-3,1;

%e 0,0,-12,-4,1;

%e 0,0,0,-20,-5,1;

%e 0,0,0,0,-30,-6,1;

%K easy,sign,tabl

%O 0,4

%A _Paul Barry_, Jul 19 2005