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A113072
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Tri-diagonal 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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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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FORMULA
| Column k has g.f. (1+x)^2*(k+1)x^k.
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EXAMPLE
| 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
| Cf. A113070, A113071.
Sequence in context: A191320 A180228 A197376 * A122918 A177424 A129903
Adjacent sequences: A113069 A113070 A113071 * A113073 A113074 A113075
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 14 2005
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