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

Author

Paul Barry, Oct 14 2005

Keywords

• easy
• nonn
• tabl

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.

Examples

			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.

Formula

Column k has g.f. (1+x)^2*(k+1)x^k.