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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 (list; table; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..97.

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

Cf. A113070, A113071.

Sequence in context: A180228 A212320 A197376 * A328025 A305326 A122918

Adjacent sequences:  A113069 A113070 A113071 * A113073 A113074 A113075

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 14 2005

STATUS

approved

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Last modified September 20 04:16 EDT 2021. Contains 347577 sequences. (Running on oeis4.)