A136745 Irregular triangle T(0,0)=1, T(1,0)=-1, T(1,1)=0, T(1,2)=1 and T(n,k) = T(n-1,k-2)-T(n-2,k).

1, -1, 0, 1, -1, 0, -1, 0, 1, 1, 0, -2, 0, -1, 0, 1, 1, 0, 2, 0, -3, 0, -1, 0, 1, -1, 0, 3, 0, 3, 0, -4, 0, -1, 0, 1, -1, 0, -3, 0, 6, 0, 4, 0, -5, 0, -1, 0, 1, 1, 0, -4, 0, -6, 0, 10, 0, 5, 0, -6, 0, -1, 0, 1, 1, 0, 4, 0, -10, 0, -10, 0, 15, 0, 6, 0, -7, 0, -1, 0, 1, -1, 0, 5, 0, 10, 0, -20, 0, -15, 0, 21, 0, 7, 0, -8, 0, -1, 0, 1, -1, 0, -5, 0, 15, 0, 20, 0

Offset: 0

Author

Roger L. Bagula, Mar 19 2008

Keywords

• easy
• tabf
• sign

Comments

Row sums are probably a repeating sequence 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0,...

This is simply A130777 with columns of zeros inserted in odd-numbered columns. - R. J. Mathar, Nov 04 2011

Examples

			1;
-1, 0, 1;
-1, 0, -1, 0, 1;
1, 0, -2, 0, -1, 0, 1;
1, 0, 2, 0, -3, 0, -1, 0, 1;
-1, 0, 3, 0, 3, 0, -4, 0, -1, 0, 1;
-1, 0, -3, 0, 6, 0, 4, 0, -5, 0, -1, 0, 1;
1, 0, -4, 0, -6, 0, 10, 0, 5, 0, -6, 0, -1, 0,1;
1, 0, 4,0, -10, 0, -10, 0, 15, 0, 6, 0, -7, 0, -1, 0, 1;
-1, 0, 5, 0, 10, 0, -20, 0, -15, 0, 21, 0, 7, 0, -8, 0, -1, 0, 1;
-1, 0, -5, 0, 15, 0,20, 0, -35, 0, -21, 0, 28, 0, 8, 0, -9, 0, -1, 0, 1;
		

Crossrefs

Cf. A130777.

Programs

Mathematica

Clear[p, x, n] p[x, 0] = 1; p[x, 1] = x^2 - 1; p[x_, n_] := p[x, n] = x^2*p[x, n - 1] - p[x, n - 2]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}];