OFFSET
1,1
COMMENTS
Matrices modeled on: {{k, -1, 0}, {-1, 0, -1}, {0, -1, 0}} K=1 is Steinbach: A066170 These are equivalent to the central variable determinant sequences: {{y-k, -1, 0}, {-1, y, -1}, {0, -1, y}}
FORMULA
m(n,m,d)=If[ n == m && n > 1 && m > 1, 0, If[n == m - 1 || n == m + 1, -1, If[n == m == 1, 3, 0]]]
EXAMPLE
Triangle begins:
{{3}},--> Det[{{3}}]=3
{3, -1},
{-1, -3, 1},
{-3, 2, 3, -1},
{1, 6, -3, -3, 1},
{3, -3, -9, 4,3, -1},
{-1, -9, 6, 12, -5, -3, 1}
MATHEMATICA
T[n_, m_, d_] := If[ n == m && n > 1 && m > 1, 0, If[n == m - 1 || n == m + 1, -1, If[n == m == 1, 3, 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}] Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}] a = Join[{M[1]}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[ d]], x], {d, 1, 10}]] Flatten[a] MatrixForm[a]
PROG
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula and Gary W. Adamson, Nov 03 2006
STATUS
approved