A168578 Coefficients of polynomials of the characteristic polynomials of two matrix systems subtracted: M(n)=Table[Table[If[m == k == 1, n, If[m == k, (-1)^n, 0]], {m, 1, n}], {k, 1, n}];M1(n)=Table[Table[ If[m == k + 1, -1, If[k == n && m == 1, n, If[m == k == n, -n, 0]]], {m, 1, n}], {k, 1, n}]

-5, 5, 4, -13, 15, -11, 19, 26, 14, 6, -31, 65, -70, 40, -17, 41, 99, 125, 85, 27, 8, -57, 175, -301, 315, -203, 77, -23, 71, 244, 476, 574, 434, 196, 44, 10, -91, 369, -876, 1344, -1386, 966, -444, 126, -29, 109, 485, 1275, 2190, 2562, 2058, 1110, 375, 65, 12

Offset

2,1

Comments

Absolute value row sums are:

{5, 9, 39, 65, 223, 385, 1151, 2049, 5631, 10241, 26623,...}.

The matrices adjusted so that they have the same determinants.

Links

Table of n, a(n) for n=2..56.

Example

{-5},
{5, 4},
{-13, 15, -11},
{19, 26, 14, 6},
{-31, 65, -70, 40, -17},
{41, 99, 125, 85, 27, 8},
{-57, 175, -301, 315, -203, 77, -23},
{71, 244, 476, 574, 434, 196, 44, 10},
{-91, 369, -876, 1344, -1386, 966, -444, 126, -29},
{109, 485, 1275, 2190, 2562, 2058, 1110, 375, 65, 12},
{-133, 671, -2035, 4125, -5874, 6006, -4422, 2310, -825, 187, -35}

Mathematica

Clear[M, M1, n, m, k, a, b, x]
M[n_] := Table[Table[If[m == k == 1, n, If[m == k, (-1)^n, 0]], {m, 1, n}], {k, 1, n}];
a = Table[If[n == 0, 1, CharacteristicPolynomial[M[n], x]], {n, 0, 12}];
M1[n_] := Table[Table[If[m == k + 1, -1, If[k == n && m == 1, n, If[m == k == n, -n, 0]]], {m, 1, n}], {k, 1, n}];
b = Table[If[n == 0, 1, CharacteristicPolynomial[M1[n], x]], {n, 0, 12}];
c = ExpandAll[(a - b)/x];
Table[CoefficientList[c[[n]], x], {n, 3, Length[a]}];
Flatten[%]

Crossrefs

Sequence in context: A261346 A011409 A255240 * A344235 A019253 A019173

Adjacent sequences: A168575 A168576 A168577 * A168579 A168580 A168581

Keyword

sign,uned

Author

Roger L. Bagula, Nov 30 2009

Status

approved