A137949 Triangular sequence of coefficients of characteristic polynomials rational matrices of a type: M(3)= {{0, -3/2, 0}, {-3/2, 0, -3/2}, {0, -3/2, 0}}.

0, 0, -1, -2, 0, 2, 0, 18, 0, -4, 128, 0, -96, 0, 8, 0, -1875, 0, 400, 0, -16, -23328, 0, 15552, 0, -1440, 0, 32, 0, 470596, 0, -96040, 0, 4704, 0, -64, 8388608, 0, -5242880, 0, 491520, 0, -14336, 0, 128, 0, -215233605, 0, 42515280, 0, -2204496, 0, 41472, 0, -256, -5000000000, 0, 3000000000, 0, -280000000

Offset

1,4

Comments

Row sums are:

{0, -1, 0, 14, 40, -1491, -9184, 379196, 3623040, -174881605, -2271154688};

Links

Table of n, a(n) for n=1..60.

Formula

M(3)= {{0, -3/2, 0}, {-3/2, 0, -3/2}, {0, -3/2, 0}} m(n,m)=If[ n == m, 0, If[n == m - 1 || n == m + 1, -d/2, 0]]->P(x,n); out_n,m=2^(n-1)*Coefficients(P(x,n)).

Example

{0},
{0, -1},
{-2, 0, 2},
{0, 18, 0, -4},
{128, 0, -96, 0, 8},
{0, -1875,
0, 400, 0, -16},
{-23328, 0,15552, 0, -1440, 0, 32},
{0, 470596, 0, -96040, 0, 4704, 0, -64},
{8388608, 0, -5242880, 0, 491520, 0, -14336, 0, 128},
{0, -215233605, 0, 42515280, 0, -2204496, 0, 41472, 0, -256},
{-5000000000, 0, 3000000000, 0, -280000000, 0, 8960000, 0, -115200, 0, 512}

Mathematica

Clear[M, T, d, a, x, a0] T[n_, m_, d_] := If[ n == m, 0, If[n == m - 1 || n == m + 1, -d/2, 0]]; 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}]; g = Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[M[1], Table[(2^(d - 1))*CoefficientList[Det[ M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; Flatten[a] MatrixForm[a]; Table[Apply[Plus, a[[n]]], {n, 1, Length[a]}] Table[Apply[Plus, Abs[a[[n]]]], {n, 1, Length[a]}]; Table[NSolve[Det[M[d] - x*IdentityMatrix[d]] == 0, x], {d, 1, 10}]; Table[x /. NSolve[Det[M[d] - x*IdentityMatrix[d]] == 0, x][[d]], {d, 1, 10}];

Crossrefs

Sequence in context: A089780 A136668 A057498 * A019214 A137668 A056615

Adjacent sequences: A137946 A137947 A137948 * A137950 A137951 A137952

Keyword

tabf,uned,sign

Author

Roger L. Bagula, Apr 30 2008

Status

approved