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A124216
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Generalized Pascal triangle.
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2
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1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 34, 16, 1, 1, 25, 90, 90, 25, 1, 1, 36, 195, 328, 195, 36, 1, 1, 49, 371, 931, 931, 371, 49, 1, 1, 64, 644, 2240, 3334, 2240, 644, 64, 1, 1, 81, 1044, 4788, 9846, 9846
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OFFSET
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0,5
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COMMENTS
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Consider the 1-parameter family of triangles with g.f. (1-x(1+y))/(1-2x(1+y)+x^2(1+k*x+y^2)). A007318 corresponds to k=2. A056241 corresponds to k=1. A124216 corresponds to k=0. Row sums are A006012. Diagonal sums are A124217.
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LINKS
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FORMULA
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G.f.: (1-x(1+y))/(1-2x(1+y)+x^2(1+y^2)); Number triangle T(n,k)=sum{j=0..n, C(n,j)C(j,2(j-k))2^(j-k)}.
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EXAMPLE
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Triangle begins
1,
1, 1,
1, 4, 1,
1, 9, 9, 1,
1, 16, 34, 16, 1,
1, 25, 90, 90, 25, 1,
1, 36, 195, 328, 195, 36, 1,
1, 49, 371, 931, 931, 371, 49, 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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