A127949 A000012 as an infinite lower triangular matrix with all 1's; A127899 = a simple transform; then A000012 * A127899. Given A051340, change all 1's to -1. Triangle read by rows, (n-1) -1's followed by "n".

1, -1, 2, -1, -1, 3, -1, -1, -1, 4, -1, -1, -1, -1, 5, -1, -1, -1, -1, -1, 6, -1, -1, -1, -1, -1, -1, 7, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 11, -1, -1, -1, -1, -1, -1

Offset: 1

Author

Gary W. Adamson, Feb 09 2007

Keywords

• tabl
• sign
• easy

Comments

For the inverse of A127949 see A126615, a harmonic triangle.

This is one way to define an inverse to A000217. - R. J. Mathar, Apr 30 2010

Examples

			First few rows of the triangle are:
1;
-1, 2;
-1, -1, 3;
-1, -1, -1, 4;
...
		

Crossrefs

Cf. A000012, A127899, A051340, A126615.

Programs

Maple

A127949 := proc(n) if issqr(1+8*n) then (sqrt(1+8*n)-1)/2 ; else -1 ; end if; end proc: seq(A127949(n),n=1..120) ; # R. J. Mathar, Apr 30 2010

Extensions

More terms from R. J. Mathar, Apr 30 2010