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

1,3

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

Links

Table of n, a(n) for n=1..72.

Example

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

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

Crossrefs

Cf. A000012, A127899, A051340, A126615.

Sequence in context: A175465 A080209 A347171 * A051340 A167407 A216764

Adjacent sequences: A127946 A127947 A127948 * A127950 A127951 A127952

Keyword

tabl,sign,easy

Author

Gary W. Adamson, Feb 09 2007

Extensions

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

Status

approved