OFFSET
1,2
COMMENTS
Matrices modeled on: {{-2 + y, -1, 0}, {-1, y, -1}, {0, -1, y}} The upper y-1 gives the Steinbach polynomials A066170.
FORMULA
m(n,n,d)=If[ n == m && n > 1 && m > 1, y, If[n == m - 1 || n == m + 1, -1, If[n == m == 1, y - 2, 0]]]; Det(m,n,m,d)=P(d,y)
EXAMPLE
Triangular sequence:
{1},
{-2, 1},
{-1, -2, 1},
{2, -2, -2, 1},
{1, 4, -3, -2, 1},
{-2, 3, 6, -4, -2, 1},
{-1, -6, 6, 8, -5, -2, 1},
{2, -4, -12,10, 10, -6, -2, 1},
{1, 8, -10, -20, 15, 12, -7, -2, 1},
{-2, 5, 20, -20, -30, 21, 14, -8, -2, 1},
{-1, -10, 15, 40, -35, -42, 28, 16, -9, -2, 1}
MATHEMATICA
T[n_, m_, d_] := If[ n == m && n >1 && m > 1, y, If[n == m - 1 || n == m + 1, -1, If[n == m == 1, y - 2, 0]]] M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; Table[M[d], {d, 1, 10}]; Table[Det[M[d]], {d, 1, 10}] a = Join[{{1}}, Table[CoefficientList[Table[Det[M[d]], {d, 1, 10}][[d]], y], {d, 1, 10}]]; Flatten[a]
PROG
CROSSREFS
KEYWORD
uned,sign
AUTHOR
Gary W. Adamson and Roger L. Bagula, Nov 03 2006
STATUS
approved