A123966 Triangle A124029 with the (0,0) entry replaced by 4.

4, 4, -1, 15, -8, 1, 56, -46, 12, -1, 209, -232, 93, -16, 1, 780, -1091, 592, -156, 20, -1, 2911, -4912, 3366, -1200, 235, -24, 1, 10864, -21468, 17784, -8010, 2120, -330, 28, -1, 40545, -91824, 89238, -48624, 16255, -3416, 441, -32, 1, 151316, -386373, 430992, -275724, 111524, -29589, 5152, -568, 36

Offset: 0

Author

Gary W. Adamson and Roger L. Bagula, Oct 28 2006

Keywords

• tabl
• sign

Comments

The entry for the empty matrix in row 0 and column 0 is replaced by 4 in comparison to the variant in A124029.

Examples

			4;
4, -1;
15, -8, 1;
56, -46,12, -1;
209, -232, 93, -16, 1;
780, -1091, 592, -156, 20, -1;
2911, -4912, 3366, -1200, 235, -24, 1;
10864, -21468, 17784, -8010, 2120, -330, 28, -1;
		

Crossrefs

Cf. A123343, A159764.

Programs

Mathematica

Clear[M, T, d, a, x]; T[n_, m_] = If[ n == m, 4, If[n == m - 1 || n == m + 1, -1, 0]]; M[d_] := Table[T[n, m], {n, 1, d}, {m, 1, d}]; Table[M[d], {d, 1, 10}]; Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[{{3}}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; Flatten[a]