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Triangle T(n,m) = 1 + F(m) + F(n-m) - F(n), read by rows, where F = A000045 is the Fibonacci sequence.
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%I #8 Feb 04 2014 01:21:59

%S 1,1,1,1,2,1,1,1,1,1,1,1,0,1,1,1,0,-1,-1,0,1,1,-1,-3,-3,-3,-1,1,1,-3,

%T -6,-7,-7,-6,-3,1,1,-6,-11,-13,-14,-13,-11,-6,1,1,-11,-19,-23,-25,-25,

%U -23,-19,-11,1,1,-19,-32,-39,-43,-44,-43,-39,-32,-19,1

%N Triangle T(n,m) = 1 + F(m) + F(n-m) - F(n), read by rows, where F = A000045 is the Fibonacci sequence.

%C Row sums are 1,2,4,4,4,0,-9,-30,-72,-154,-308,...

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 1, 1, 1;

%e 1, 1, 0, 1, 1;

%e 1, 0, -1, -1, 0, 1;

%e 1, -1, -3, -3, -3, -1, 1;

%e 1, -3, -6, -7, -7, -6, -3, 1;

%e 1, -6, -11, -13, -14, -13, -11, -6, 1;

%e 1, -11, -19, -23, -25, -25, -23, -19, -11, 1;

%e 1, -19, -32, -39, -43, -44, -43, -39, -32, -19, 1;

%t L[n_, m_] = Fibonacci[m] + Fibonacci[n - m] - (Fibonacci[0] + Fibonacci[n]) + 1;

%t Table[Table[L[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K sign,tabl,easy

%O 0,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Apr 07 2010