A122947 Triangular sequence: 1, 1 - x, -1 - x + x^2, 1 + 3 x + x^2 - x^3, 1 - x - 4 x^2 - x^3 +x^4, -1 - x + 6 x^2 + 8 x^3 + x^4 - x^5, -1 + 3 x + 6 x^2 - 7 x^3 - 10 x^4 - x^5 + x^6.

1, 1, -1, -1, -1, 1, 1, 3, 1, -1, 1, -1, -4, -1, 1, -1, -1, 6, 8, 1, -1, -1, 3, 6, -7, -10, -1, 1, -1, 7, -6, -14, 8, 12, 1, -1, 1, 1, -13, 8, 20, -8, -13, -1, 1, -1, -3, 11, 17, -36, -26, 27, 21, 1, -1, -1, 1, 19, -26, -53, 63, 53, -32, -25, -1, 1, -1, 5, 15, -89, 54, 144, -102, -92, 37, 29, 1, -1, 1, 3, -27, -10, 169, -89, -226, 127, 121

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Oct 24 2006

Keywords

• tabl
• uned
• less
• sign

Comments

Matrices: 1

X 1 {{1}}

2 X 2 {{1, 1}, {1, 0}}

3 X 3 {{1, 1, 1}, {1, 0, 1}, {1, 1, 0}}

4 X 4 {{1, 1, 1, 1}, {1, 0, 1, 0}, {1, 1, 0, 0}, {1, 0, 0, 0}}

5 X 5 {{1, 1, 1, 1, 1}, {1, 0, 1, 0, 1}, {1, 1, 0, 0, 1}, {1, 0, 0, 0, 1}, {1, 1, 1, 1, 0}}

6 X 6 {{1, 1, 1, 1, 1, 1}, {1, 0, 1, 0, 1, 0}, {1, 1, 0, 0, 1, 1}, {1, 0, 0, 0, 1, 0}, {1, 1, 1, 1, 0, 0}, {1, 0, 1, 0, 0, 0}}

Examples

			Triangle sequence:
{1},
{1, -1},
{-1, -1, 1},
{1, 3, 1, -1},
{1, -1, -4, -1, 1},
{-1, -1, 6, 8, 1, -1},
{-1, 3, 6, -7, -10, -1, 1},
{-1, 7, -6, -14, 8, 12, 1, -1}
		

Programs

Mathematica

c[i_, k_] := Floor[Mod[i/2^k, 2]];
An[d_] := Table[If[Sum[c[n, k]*c[m, k], {k, 0, d - 1}] == 0, 1, 0], {n, 0, d - 1}, {m, 0, d - 1}]; Join[{{1}},
Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d,1, 20}]];
Flatten[%]