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%I #2 Mar 30 2012 17:34:35
%S -5,5,4,-13,15,-11,19,26,14,6,-31,65,-70,40,-17,41,99,125,85,27,8,-57,
%T 175,-301,315,-203,77,-23,71,244,476,574,434,196,44,10,-91,369,-876,
%U 1344,-1386,966,-444,126,-29,109,485,1275,2190,2562,2058,1110,375,65,12
%N 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}]
%C Absolute value row sums are:
%C {5, 9, 39, 65, 223, 385, 1151, 2049, 5631, 10241, 26623,...}.
%C The matrices adjusted so that they have the same determinants.
%e {-5},
%e {5, 4},
%e {-13, 15, -11},
%e {19, 26, 14, 6},
%e {-31, 65, -70, 40, -17},
%e {41, 99, 125, 85, 27, 8},
%e {-57, 175, -301, 315, -203, 77, -23},
%e {71, 244, 476, 574, 434, 196, 44, 10},
%e {-91, 369, -876, 1344, -1386, 966, -444, 126, -29},
%e {109, 485, 1275, 2190, 2562, 2058, 1110, 375, 65, 12},
%e {-133, 671, -2035, 4125, -5874, 6006, -4422, 2310, -825, 187, -35}
%t Clear[M, M1, n, m, k, a, b, x]
%t M[n_] := Table[Table[If[m == k == 1, n, If[m == k, (-1)^n, 0]], {m, 1, n}], {k, 1, n}];
%t a = Table[If[n == 0, 1, CharacteristicPolynomial[M[n], x]], {n, 0, 12}];
%t 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}];
%t b = Table[If[n == 0, 1, CharacteristicPolynomial[M1[n], x]], {n, 0, 12}];
%t c = ExpandAll[(a - b)/x];
%t Table[CoefficientList[c[[n]], x], {n, 3, Length[a]}];
%t Flatten[%]
%K sign,uned
%O 2,1
%A _Roger L. Bagula_, Nov 30 2009
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