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A115633 A divide and conquer-related triangle. 4
1, 1, -1, -4, 0, 1, 0, 0, 1, -1, 0, -4, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, -4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -4, 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, -4, 0, 0, 0, 0, 0, 0, 0, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are A115634. Diagonal sums are A115635. Inverse is A115636.

LINKS

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

FORMULA

G.f.: (1+x-xy)/(1-x^2*y^2)-4x^2/(1-x^2*y); (1, -x)+(x, x)/2+(x, -x)/2-4(x^2, x^2) expressed in the notation of stretched Riordan arrays; Column k has g.f. (-x)^k+(x(-x)^k+x^(k+1))/2-4x^(2k+2); T(n, k)=(-1)^n*(if(n=k, 1, 0) OR if(n=2k+2, -4, 0) OR if(n=k+1, -(1+(-1)^k)/2, 0));

EXAMPLE

Triangle begins

1,

1, -1,

-4, 0, 1,

0, 0, 1, -1,

0, -4, 0, 0, 1,

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

0, 0, -4, 0, 0, 0, 1,

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

0, 0, 0, -4, 0, 0, 0, 0, 1,

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

0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1,

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

0, 0, 0, 0, 0, -4, 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, -4, 0, 0, 0, 0, 0, 0, 0, 1,

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

0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 1

CROSSREFS

Sequence in context: A321188 A322076 A115713 * A199571 A036859 A036861

Adjacent sequences:  A115630 A115631 A115632 * A115634 A115635 A115636

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Jan 27 2006

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)