This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%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