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A112466
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Riordan array ((1+2x)/(1+x),x/(1+x)).
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2
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1, 1, 1, -1, 0, 1, 1, -1, -1, 1, -1, 2, 0, -2, 1, 1, -3, 2, 2, -3, 1, -1, 4, -5, 0, 5, -4, 1, 1, -5, 9, -5, -5, 9, -5, 1, -1, 6, -14, 14, 0, -14, 14, -6, 1, 1, -7, 20, -28, 14, 14, -28, 20, -7, 1, -1, 8, -27, 48, -42, 0, 42, -48, 27, -8, 1, 1, -9, 35, -75, 90, -42, -42, 90, -75, 35, -9, 1, -1, 10, -44, 110, -165, 132, 0, -132, 165, -110, 44
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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COMMENTS
| Row sums are (1,2,0,0,0,....). Diagonal sums are (-1)^(n+1)*F(n-2). Inverse is A112465. T(2n,n)=0.
Triangle T(n,k), 0<=k<=n, read by rows, given by [1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 07 2006
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REFERENCES
| E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Mathematics, 34 (2005) pp. 101-122.
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FORMULA
| Number triangle T(n, k)=(C(n, n-k)-2*C(n-1, n-k-1))*(-1)^(n-k)
Sum_{k, 0<=k<=n} T(n, k)*x^k = (x+1)*(x-1)^(n-1), for n>=1. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 03 2005
T(0,0)=T(1,0)=T(1,1)=1, T(n,k)=0 if n<0 or if n<k, T(n,k)=T(n-1,k-1)-T(n-1,k)for n>1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 26 2006
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EXAMPLE
| Triangle starts
1;
1,1;
-1,0,1;
1,-1,-1,1;
-1,2,0,-2,1;
1,-3,2,2,-3,1;
-1,4,-5,0,5,-4,1;
Production matrix begins
1, 1,
-2, -1, 1,
2, 0, -1, 1,
-2, 0, 0, -1, 1,
2, 0, 0, 0, -1, 1,
-2, 0, 0, 0, 0, -1, 1,
2, 0, 0, 0, 0, 0, -1, 1
[Paul Barry, April 8 2011]
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CROSSREFS
| Cf. A008482, A037012, A112467.
Sequence in context: A008482 A037012 A112467 * A166348 A127543 A068907
Adjacent sequences: A112463 A112464 A112465 * A112467 A112468 A112469
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 06 2005
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EXTENSIONS
| Corrected second comment. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 11 2008
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