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A090842
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Square array of numbers read by antidiagonals where T(n,k)=((k+3)(k+2)^n-2)/(k+1)
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1
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1, 1, 4, 1, 5, 10, 1, 6, 17, 22, 1, 7, 26, 53, 46, 1, 8, 37, 106, 161, 94, 1, 9, 50, 187, 426, 485, 190, 1, 10, 65, 302, 937, 1706, 1457, 382, 1, 11, 82, 457, 1814, 4687, 6826, 4373, 766, 1, 12, 101, 658, 3201, 10886, 23437, 27306, 13121, 1534, 1, 13, 122, 911, 5266
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OFFSET
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0,3
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COMMENTS
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Nodes on a tree with degree k interior nodes and degree 1 boundary nodes.
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REFERENCES
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L. He, X. Liu and G. Strang, (2003) Trees with Cantor Eigenvalue Distribution. Studies in Applied Mathematics 110 (2), 123-138
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LINKS
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FORMULA
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The total number of nodes on a tree with degree k interior nodes and degree 1 boundary nodes is given by N(k, r)=(k(k-1)^r-2))/(k-2).
G.f.: Sum_{k>=0} (1+x*y)/(1-x*y)/(1-(k+2)*x*y)*y^k. - Vladeta Jovovic, Dec 12 2003
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EXAMPLE
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Rows begin
1 4 10 22 ...
1 5 17 53 ...
1 6 26 106 ...
1 7 37 187 ...
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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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