A068344 Square array read by antidiagonals of T(n,k) = sign(n-k).

0, -1, 1, -1, 0, 1, -1, -1, 1, 1, -1, -1, 0, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 0, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 0, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 0, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1

Offset

0,1

Links

Table of n, a(n) for n=0..101.

Formula

a(n-1) = sign(A002260(n) - A004736(n)) or a(n-1) = sign((n-t*(t+1)/2) - ((t*t+3*t+4)/2-n)) where t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 24 2012

Example

The start of the array is:
   0;
  -1,   1;
  -1,   0,   1;
  -1,  -1,   1,   1;
  -1,  -1,   0,   1,   1;
  ...
- Boris Putievskiy, Dec 24 2012

Crossrefs

Cf. A049581, A057427, A057428, A002260, A004736. As a straight sequence, a(n)=0 when n is in A046092. A023532 seen as a triangle is half this square.

Sequence in context: A285596 A257680 A323377 * A161382 A138886 A269528

Adjacent sequences: A068341 A068342 A068343 * A068345 A068346 A068347

Keyword

easy,sign,tabl

Author

Henry Bottomley, Mar 06 2002

Status

approved