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A097807
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Riordan array (1/(1+x),1) read by rows.
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10
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1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Columns have g.f. x^k/(1+x). Row sums are A059841. Diagonal sums are (-1)^n*A008619 with g.f. 1/((1+x)(1-x^2)). Inverse of A097806. A097807=B^(-1)*A097805, where B is the binomial matrix.
Seen as a recursive table this array is related to A051731 via its recurrence relation. By changing the initial condition in the formula below from =if(row()=column();1;... to =if(row()=1;1;... we get A051731 rotated 90 degrees to the right. [From Mats Granvik (mats.granvik(AT)abo.fi), Apr 06 2010]
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FORMULA
| Triangle array of numbers T(n, k) with T(n, k)=if(n>=k, (-1)^(n-k), 0).
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EXAMPLE
| Rows begin {1}, {-1,1}, {1,-1,1}, {-1,1,-1,1}, {1,-1,1,-1,1},....
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PROG
| (Other) (Excel cell formula) =if(row()=column(); 1; if(row()=1; 0; sum(indirect(address(row()-1; column()+1)&":"&address(row()-1; column()+row()-1)))-sum(indirect(address(row(); column()+1)&":"&address(row(); column()+row()-1))))) [From Mats Granvik (mats.granvik(AT)abo.fi), Apr 06 2010]
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CROSSREFS
| Cf. A051731. [From Mats Granvik (mats.granvik(AT)abo.fi), Apr 06 2010]
Sequence in context: A108784 A020985 A034947 * A014077 A174351 A181432
Adjacent sequences: A097804 A097805 A097806 * A097808 A097809 A097810
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Aug 25 2004
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