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1, 1, 1, 3, 4, 1, 3, 9, 7, 1, 3, 12, 18, 10, 1, 3, 15, 30, 30, 13, 1, 3, 18, 45, 60, 45, 16, 1, 3, 21, 63, 105, 105, 63, 19, 1, 3, 24, 84, 168, 210, 168, 84, 22, 1
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OFFSET
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0,4
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COMMENTS
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Row sums = A131128: (1, 2, 8, 20, 44, 92, 188, 380, ...), the binomial transform of (1, 1, 5, 1, 5, 1, 5, ...). Triangle A131108 has row sums (1, 2, 6, 14, 30, 62, ...), the binomial transform of (1, 1, 3, 1, 3, 1, ...). Generalization: Given triangles generated from N*A007318 - (N-1)*A097806, row sums are binomial transforms of (1, 1, (2N-1), 1, (2N-1), 1, ...).
Triangle T(n,k), 0 <= k <= n, read by rows given by [1,2,-3,1,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 18 2007
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LINKS
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FORMULA
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G.f.: (1-x*y+2*x^2+2*x^2*y)/((-1+x+x*y)*(x*y-1)). - R. J. Mathar, Aug 12 2015
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EXAMPLE
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First few rows of the triangle:
1;
1, 1;
3, 4, 1;
3, 9, 7, 1;
3, 12, 18, 10, 1;
3, 15, 30, 30, 13, 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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