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%I #10 Aug 09 2015 01:15:03
%S 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,
%T -13,2,1,-1,16,40,-52,-24,16,2,-1,1,-20,-70,86,87,-30,-19,2,1,1,-25,
%U -100,190,150,-131,-36,22,2,-1,-1,30,155,-294,-403,232,184,-42,-25,2,1,-1,36,210,-553,-656,736,332,-246,-48,28,2,-1,1,-42
%N Triangular sequence from the characteristic polynomials of the SL(n,Z)/ determinants {1,-1} type triantidiagonal 2 center with one upper, -1 side antidiagonal above and below: M(3)={{0, -1, 1}, {-1, 2, -1}, {2, -1, 0}}.
%C 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}}
%F 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}];
%e Triangular sequence:
%e {1},
%e {1, -1},
%e {-1, 2, 1},
%e {-1, 4, 2, -1},
%e {1, -6, -7, 2, 1},
%e {1, -9, -12, 10, 2, -1},
%e {-1, 12, 26, -18, -13, 2, 1},
%e {-1, 16, 40, -52, -24,16, 2, -1},
%e {1, -20, -70, 86, 87, -30, -19, 2, 1}
%t 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[%]
%K sign,tabl,uned
%O 1,5
%A _Gary W. Adamson_ and _Roger L. Bagula_, Oct 31 2006
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