0,5

Row sums are:

{1, -2, 3, 0, -27, 162, -729, 2916, -10935, 39366, -137781,...}.

These matrices are an all ones matrix with central diagonal negative.

These matrices have the odd orthogonality property of:

M(n).M(n)-M(n)-(-5+n)*Ones(n)=6*IdentityMatirix[n];

Table[T[n, m, d], {n, 1, d}, {m, 1, d}].Table[T[n, m, d], {n, 1, d}, {m, 1, d}]

- Table[T[n, m, d], {n, 1, d}, {m, 1, d}]

- (-5 + d)*Table[1, {n, d}, {m, d}]

Matrix example:

M(3)={{-1, 1, 1},

{1, -1, 1},

{1, 1, -1}}

M(d)=If[ m == n, -1, 1];

out_(n,m)=coefficients(characteristicpolynomial(M(n),x),x)

{1},

{-1, -1},

{0, 2, 1},

{4, 0, -3, -1},

{-16, -16, 0, 4, 1},

{48, 80, 40, 0, -5, -1},

{-128, -288, -240, -80, 0, 6, 1},

{320, 896, 1008, 560, 140, 0, -7, -1},

{-768, -2560, -3584, -2688, -1120, -224, 0, 8, 1},

{1792, 6912, 11520, 10752, 6048, 2016, 336, 0, -9, -1},

{-4096, -17920, -34560, -38400, -26880, -12096, -3360, -480, 0, 10, 1}

Clear[M, T, d, a, x, a0];

T[n_, m_, d_] := If[ m == n, -1, 1];

M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}];

a0 = Table[M[d], {d, 1, 10}];

Table[Det[M[d]], {d, 1, 10}];

Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];

a = Join[{{1}}, Table[CoefficientList[Expand[CharacteristicPolynomial[M[n], x]], x], {n, 1, 10}]];

Flatten[a]

Join[{1}, Table[Apply[Plus, CoefficientList[Expand[CharacteristicPolynomial[M[ n], x]], x]], {n, 1, 10}]];

Sequence in context: A087569 A048614 A001442 this_sequence A059781 A087664 A158032

Adjacent sequences: A158282 A158283 A158284 this_sequence A158286 A158287 A158288

sign,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 15 2009