A130194 Let M = lower triangular matrix with 1's on and below the main diagonal, with columns multiplied by +1, +1, -1, -1, repeated; form M^2; read across rows of resulting triangle.

1, 2, 1, -1, 2, 1, -4, -1, 2, 1, 1, -4, -1, 2, 1, 6, 1, -4, -1, 2, 1, -1, 6, 1, -4, -1, 2, 1, -8, -1, 6, 1, -4, -1, 2, 1, 1, -8, -1, 6, 1, -4, -1, 2, 1, 10, 1, -8, -1, 6, 1, -4, -1, 2, 1, -1, 10, 1, -8, -1, 6, 1, -4, -1, 2, 1, -12, -1, 10, 1, -8, -1, 6, 1, -4, -1, 2, 1

Offset: 1

Author

Gary W. Adamson, May 16 2007

Keywords

• tabl
• sign

Comments

A000012(signed)^2.

Left border = A009531: (1, 2, -1, -4, 1, 6, -1, ...).

Row sums = A130195: (1, 3, 2, -2, -1, 5, 4, ...).

Row sums of the unsigned triangle = A058074: (1, 3, 4, 8, 9, 15, ...).

A009531 in every column: (1, 2, -1, -4, 1, 6, -1, ...).

Examples

			First few rows of the triangle:
   1;
   2,  1;
  -1,  2,  1;
  -4, -1,  2,  1;
   1, -4, -1,  2,  1;
   6,  1, -4, -1,  2,  1;
  ...
		

Crossrefs

Cf. A000012, A058074, A009531.

Programs

PARI

trg(nn) = {vgf = x*(1+x)^2/(1+x^2)^2 + O(x^(nn+1)); m = matrix(nn, nn, i, j, if (i >= j, polcoeff(vgf, i-j+1))); for (n=1, nn, for (k=1, n, print1(m[n, k], ", ");); print(););} \\ Michel Marcus, Oct 03 2014

Extensions

More terms from Michel Marcus, Oct 03 2014