A124018 Triangle T(n,k) = A136451(n,k), except T(0,0)=2.

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

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Oct 31 2006

Keywords

• tabl
• sign
• less

Comments

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.

Examples

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

Programs

Mathematica

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[%]