A115359 Matrix (1,x)-(x,x^2) in Riordan array notation.

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

Offset

0,1

Comments

Row sums are 1,0,1,0,1,0... Diagonal sums are A115360. Inverse is A115361.

Links

Table of n, a(n) for n=0..119.

Formula

Number triangle T(n, k)=if(n=k, 1, 0) OR if(n=2k+1, -1, 0).

Example

Triangle begins:
   1;
  -1,  1;
   0,  0,  1;
   0, -1,  0,  1;
   0,  0,  0,  0,  1;
   0,  0, -1,  0,  0, 1;
   0,  0,  0,  0,  0, 0, 1;
   0,  0,  0, -1,  0, 0, 0, 1;
   0,  0,  0,  0,  0, 0, 0, 0, 1;
   0,  0,  0,  0, -1, 0, 0, 0, 0, 1;
  ...

Prog

(PARI) tabl(nn) = {T = matrix(nn, nn, n, k, n--; k--; if ((n==k), 1, if (n==2*k+1, -1, 0))); for (n=1, nn, for (k=1, n, print1(T[n, k], ", "); ); print(); ); } \\ Michel Marcus, Mar 28 2015

Crossrefs

Sequence in context: A256538 A074910 A115356 * A117906 A090678 A110037

Adjacent sequences: A115356 A115357 A115358 * A115360 A115361 A115362

Keyword

easy,sign,tabl

Author

Paul Barry, Jan 21 2006

Status

approved