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A181650
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Inverse of number triangle A070909.
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2
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1, -1, 1, -1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1
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OFFSET
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0,1
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COMMENTS
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Generalized (conditional) Riordan array with k-th column generated by x^k*(1-x-x^2) if k is even, x^k otherwise.
Triangle T(n,k), read by rows, given by (-1,2,-1/2,-1/2,0,0,0,0,0,0,0,...) DELTA (1,0,-1,0,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 19 2011
Double Riordan array (1 - x - x^2; x/(1 - x - x^2), x*(1 - x - x^2)) as defined in Davenport et al. - Peter Bala, Aug 15 2021
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LINKS
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D. E. Davenport, L. W. Shapiro and L. C. Woodson, The Double Riordan Group, The Electronic Journal of Combinatorics, 18(2) (2012).
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FORMULA
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EXAMPLE
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Triangle begins
1,
-1, 1,
-1, 0, 1,
0, 0, -1, 1,
0, 0, -1, 0, 1,
0, 0, 0, 0, -1, 1,
0, 0, 0, 0, -1, 0, 1,
0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, -1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1
Production matrix begins
-1, 1,
-2, 1, 1,
-1, 1, -1, 1,
-1, 1, -2, 1, 1,
-1, 1, -1, 1, -1, 1,
-1, 1, -1, 1, -2, 1, 1,
-1, 1, -1, 1, -1, 1, -1, 1,
-1, 1, -1, 1, -1, 1, -2, 1, 1,
-1, 1, -1, 1, -1, 1, -1, 1, -1, 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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