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A115633
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A divide and conquer-related triangle.
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3
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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; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums are A115634. Diagonal sums are A115635. Inverse is A115636.
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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));
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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
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CROSSREFS
| Sequence in context: A101453 A128131 A115713 * A199571 A036859 A036861
Adjacent sequences: A115630 A115631 A115632 * A115634 A115635 A115636
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 27 2006
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