OFFSET
1,5
COMMENTS
Matrices: {{1}}, {{-1, 1}, {2, -1}}, {{0, -1, 1}, {-1, 2, -1}, {2, -1, 0}}, {{0, 0, -1, 1}, {0, -1, 2, -1}, {-1, 2, -1, 0}, {2, -1, 0, 0}}, {{0, 0, 0, -1, 1}, {0, 0, -1, 2, -1}, {0, -1, 2, -1, 0}, {-1, 2, -1, 0, 0}, {2, -1, 0, 0,0}}
FORMULA
k=2; m(n,m,d)= = Table[If[n +m - 1 == d && n > 1, k, If[n + m == d, -1, If[n + m - 2 == d, -1, If[n == 1 && m == d, k - 1, 0]]]], {n, 1, d}, {m, 1, d}];
EXAMPLE
Triangular sequence:
{1},
{1, -1},
{-1, 2, 1},
{-1, 4, 2, -1},
{1, -6, -7, 2, 1},
{1, -9, -12, 10, 2, -1},
{-1, 12, 26, -18, -13, 2, 1},
{-1, 16, 40, -52, -24,16, 2, -1},
{1, -20, -70, 86, 87, -30, -19, 2, 1}
MATHEMATICA
k = 2; An[d_] := Table[If[n + m - 1 == d && n > 1, k, If[n + m == d, -1, If[n + m - 2 == d, -1, If[n == 1 &&m == d, k - 1, 0]]]], {n, 1, d}, {m, 1, d}]; Join[An[1], Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson and Roger L. Bagula, Oct 31 2006
STATUS
approved