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A155726 Production matrix for Fibonacci numbers, read by row.

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%I A155726 #9 Apr 02 2019 05:43:27
%S A155726 0,1,2,-1,1,3,0,-1,1,4,0,0,-1,1,5,0,0,0,-1,1,6,0,0,0,0,-1,1,7,0,0,0,0,
%T A155726 0,-1,1,8,0,0,0,0,0,0,-1,1,9,0,0,0,0,0,0,0,-1
%N A155726 Production matrix for Fibonacci numbers, read by row.
%C A155726 The matrix generated by this matrix has row sums F(n+1).
%H A155726 E. Deutsch, L. Ferrari and S. Rinaldi, <a href="https://doi.org/10.1016/j.aam.2004.05.002">Production Matrices</a>, Advances in Applied Mathematics, 34 (2005) pp. 101-122.
%e A155726 Matrix begins
%e A155726   0, 1,
%e A155726   2, -1, 1,
%e A155726   3, 0, -1, 1,
%e A155726   4, 0, 0, -1, 1,
%e A155726   5, 0, 0, 0, -1, 1,
%e A155726   6, 0, 0, 0, 0, -1, 1,
%e A155726   7, 0, 0, 0, 0, 0, -1, 1,
%e A155726   8, 0, 0, 0, 0, 0, 0, -1, 1,
%e A155726   9, 0, 0, 0, 0, 0, 0, 0, -1, 1
%e A155726 The row augmented triangular matrix
%e A155726   1,
%e A155726   0, 1,
%e A155726   2, -1, 1,
%e A155726   3, 0, -1, 1,
%e A155726   4, 0, 0, -1, 1,
%e A155726   5, 0, 0, 0, -1, 1,
%e A155726   6, 0, 0, 0, 0, -1, 1,
%e A155726   7, 0, 0, 0, 0, 0, -1, 1,
%e A155726   8, 0, 0, 0, 0, 0, 0, -1, 1,
%e A155726   9, 0, 0, 0, 0, 0, 0, 0, -1, 1
%e A155726 has row sums 0^n+n. Its inverse has row sums (n+1)(2-n)/2 or A080956.
%e A155726 This is the matrix
%e A155726     1,
%e A155726     0, 1,
%e A155726    -2, 1, 1,
%e A155726    -5, 1, 1, 1,
%e A155726    -9, 1, 1, 1, 1,
%e A155726   -14, 1, 1, 1, 1, 1,
%e A155726   -20, 1, 1, 1, 1, 1, 1,
%e A155726   -27, 1, 1, 1, 1, 1, 1, 1,
%e A155726   -35, 1, 1, 1, 1, 1, 1, 1, 1
%e A155726 with first column (n+2)(1-n)/2.
%Y A155726 Cf. A080956, A155727.
%K A155726 sign,tabf
%O A155726 0,3
%A A155726 _Paul Barry_, Jan 25 2009