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Search: id:A115524
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| A115524 |
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Number triangle (1,-x)+(x,x)/2+(x,-x)/2-(x^2,x^2) (expressed using the notation of stretched Riordan arrays). |
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+0
4
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| 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; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are A000007. Diagonal sums are A115525. Matrix inverse is A115526. Row sums of inverse are A023416(n+2).
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FORMULA
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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 (pbarry(AT)wit.ie), Feb 02 2006
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EXAMPLE
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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,
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CROSSREFS
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Sequence in context: A010056 A155898 A115952 this_sequence A117198 A054525 A065333
Adjacent sequences: A115521 A115522 A115523 this_sequence A115525 A115526 A115527
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 25 2006
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