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A113072
Tridiagonal matrix associated with coordination sequences.
0
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
OFFSET
0,2
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.
FORMULA
Column k has g.f. (1+x)^2*(k+1)x^k.
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;
CROSSREFS
Sequence in context: A180228 A212320 A197376 * A328025 A305326 A122918
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Oct 14 2005
STATUS
approved