A124018 - OEIS

%I #7 Oct 12 2012 14:55:30

%S 2,2,-1,-3,2,1,-4,6,2,-1,5,-10,-9,2,1,6,-19,-16,12,2,-1,-7,28,42,-22,

%T -15,2,1,-8,44,68,-74,-28,18,2,-1,9,-60,-138,126,115,-34,-21,2,1,10,

%U -85,-208,316,202,-165,-40,24,2,-1,-11,110,363,-506,-605,296,224,-46,-27,2,1,-12,146,518,-1059,-1008,1032,408,-292,-52

%N Triangle T(n,k) = A136451(n,k), except T(0,0)=2.

%C This triangle here assigns the characteristic polynomial 2 to the matrix with 0 columns and zero rows, in the spirit of keeping a "virtual" 2 on the antidiagonals of these tri-antidiagonal matrices.

%e 2;

%e 2, -1;

%e -3,2, 1;

%e -4, 6, 2, -1;

%e 5, -10, -9, 2, 1;

%e 6, -19, -16, 12, 2, -1;

%e -7,28, 42, -22, -15, 2, 1;

%e -8, 44, 68, -74, -28,18, 2, -1;

%e 9, -60, -138, 126, 115, -34, -21, 2, 1;

%t An[d_] := Table[If[n + m - 1 == d, 2, 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 tabl,sign,less

%O 0,1

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 31 2006