A113072 Tridiagonal matrix associated with coordination sequences.

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.

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