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A113072
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Tridiagonal matrix associated with coordination sequences.
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0
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1, 2, 2, 1, 4, 3, 0, 2, 6, 4, 0, 0, 3, 8, 5, 0, 0, 0, 4, 10, 6, 0, 0, 0, 0, 5, 12, 7, 0, 0, 0, 0, 0, 6, 14, 8, 0, 0, 0, 0, 0, 0, 7, 16, 9, 0, 0, 0, 0, 0, 0, 0, 8, 18, 10, 0, 0, 0, 0, 0, 0, 0, 0, 9, 20, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 22, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 24, 13, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,2
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COMMENTS
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Coefficient array of expansion of ((1+x)/(1-r*x))^2, or self-convolution of coordination sequence for the infinite tree with valency r. Row sums are A008574, (coordination sequence for square lattice). Diagonal sums are A000027.
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LINKS
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FORMULA
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Column k has g.f. (1+x)^2*(k+1)x^k.
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EXAMPLE
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Triangle begins
1;
2, 2;
1, 4, 3;
0, 2, 6, 4;
0, 0, 3, 8, 5;
0, 0, 0, 4, 10, 6;
0, 0, 0, 0, 5, 12, 7;
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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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