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%I #6 Mar 04 2018 21:19:44
%S 1,1,-1,-1,-2,1,-3,1,3,-1,-1,8,0,-4,1,5,7,-14,-2,5,-1,7,-14,-21,20,5,
%T -6,1,-3,-35,21,45,-25,-9,7,-1,-17,-4,98,-16,-80,28,14,-8,1,-11,83,60,
%U -204,-14,126,-28,-20,9,-1,23,102,-219,-232,350,84,-182,24,27,-10,1
%N Triangle of coefficients of characteristic polynomials of asymmetrical tridiagonal matrices: Middle diagonal: a=1; Lower first subdiagonal: b=2; Upper first subdiagonal: c=1; Example: M(3) {{1, 1, 0}, {2, 1, 1}, {0, 2, 1}}.
%C Row sums are:
%C {1, 0, -2, 0, 4, 0, -8, 0, 16, 0, -32}
%D Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, 1978, ISBN 0070511586, see p. 516.
%F a(n)= 1; b(n)= 2; c(n) = 1; T(n, m, d) := If[ n == m,a(n), If[n == m - 1 || n == m + 1, If[n == m - 1, c(m - 1), If[n == m + 1, b(n - 1), 0]], 0]];
%e {1},
%e {1, -1},
%e {-1, -2, 1},
%e {-3, 1, 3, -1},
%e {-1, 8, 0, -4, 1},
%e {5, 7, -14, -2, 5, -1},
%e {7, -14, -21, 20, 5, -6, 1},
%e {-3, -35, 21, 45, -25, -9, 7, -1},
%e {-17, -4, 98, -16, -80, 28, 14, -8, 1},
%e {-11, 83, 60, -204, -14,126, -28, -20, 9, -1},
%e {23, 102, -219, -232, 350, 84, -182, 24, 27, -10, 1}
%t a[n_] := 1; b[n_] := 2; c[n_] = 1; T[n_, m_, d_] := If[ n == m,a[n], If[n == m - 1 || n == m + 1, If[n == m - 1, c[m - 1], If[n == m + 1, b[n - 1], 0]], 0]]; MO[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; a0 = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[MO[n], x], x], {n, 1, 10}]]; Flatten[a0]
%K uned,tabl,sign
%O 1,5
%A _Roger L. Bagula_, Mar 31 2008
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