A115524 Number triangle (1,-x)+(x,x)/2+(x,-x)/2-(x^2,x^2) (expressed using the notation of stretched Riordan arrays).

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

Offset

0,1

Comments

Row sums are A000007. Diagonal sums are A115525. Matrix inverse is A115526. Row sums of inverse are A023416(n+2).

Links

Table of n, a(n) for n=0..120.

Formula

Column k has g.f. (-x)^k+(x(-x)^k+x^(k+1))/2-x^(2k+2); Number triangle T(n, k)=(-1)^n*(if(n=k, 1, 0) OR if(n=2k+2, -1, 0) OR if(n=k+1, -(1+(-1)^k)/2, 0)).

G.f.: (1+x-x*y)/(1-x^2*y^2)-x^2/(1-x^2*y); - Paul Barry, Feb 02 2006

Example

Triangle begins
1,
1, -1,
-1, 0, 1,
0, 0, 1, -1,
0, -1, 0, 0, 1,
0, 0, 0, 0, 1, -1,
0, 0, -1, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 1, -1,
0, 0, 0, -1, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
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, 1, -1,

Crossrefs

Sequence in context: A155898 A181650 A115952 * A370122 A117198 A271047

Adjacent sequences: A115521 A115522 A115523 * A115525 A115526 A115527

Keyword

easy,sign,tabl

Author

Paul Barry, Jan 25 2006

Status

approved