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A115524 Number triangle (1,-x)+(x,x)/2+(x,-x)/2-(x^2,x^2) (expressed using the notation of stretched Riordan arrays). 3
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A117198 A271047 A054525

Adjacent sequences:  A115521 A115522 A115523 * A115525 A115526 A115527

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Jan 25 2006

STATUS

approved

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Last modified October 15 07:46 EDT 2019. Contains 328026 sequences. (Running on oeis4.)