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%I #7 Aug 03 2013 03:59:24
%S 4,4,-1,-15,2,1,-56,18,4,-1,209,-34,-33,2,1,780,-259,-128,36,4,-1,
%T -2911,484,738,-70,-51,2,1,-10864,3620,2824,-842,-200,54,4,-1,40545,
%U -6756,-14178,1614,1591,-106,-69,2,1,151316,-50437,-53888,16564,6164,-1749,-272,72,4,-1,-564719,94118,251811,-31514,-39629
%N Center antidiagonal four in a tri-antidiagonal n-th Matrix generated triangular sequence: first element as 4==m[1,1,1].
%C These matrices and triangular sequences are machine generated: all we have done is invent the matrix form "tri-antidiagonal matrices" and get a way to compute it. Matrices: {{4}}, {{-1, 4}, {4, -1}}, {{0, -1, 4}, {-1, 4, -1}, {4, -1, 0}}, {{0, 0, -1, 4}, {0, -1, 4, -1}, {-1, 4, -1, 0}, {4, -1, 0, 0}}, {{0, 0, 0, -1, 4}, {0, 0, -1, 4, -1}, {0, -1, 4, -1, 0}, {-1, 4, -1, 0, 0}, {4, -1, 0, 0,0}}
%F m(n,m,d)=If[n + m - 1 == d, 4, If[n + m == d, -1, If[n + m - 2 == d, -1, 0]]]
%e Triangular sequence:
%e {4},
%e {4, -1},
%e {-15, 2, 1},
%e {-56, 18, 4, -1},
%e {209, -34, -33, 2, 1},
%e {780, -259, -128, 36, 4, -1},
%e {-2911, 484, 738, -70, -51, 2, 1},
%e {-10864, 3620, 2824, -842, -200, 54, 4, -1},
%e {40545, -6756, -14178, 1614, 1591, -106, -69, 2, 1}
%t An[d_] := Table[If[n + m - 1 == d, 4, If[n + m == d, -1, If[n + m - 2 == d, -1, 0]]], {n, 1, d}, {m, 1, d}]; Join[An[1], Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]
%K uned,sign
%O 1,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 01 2006
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