A090842 Square array of numbers read by antidiagonals where T(n,k) = ((k+3)*(k+2)^n-2)/(k+1).

1, 1, 4, 1, 5, 10, 1, 6, 17, 22, 1, 7, 26, 53, 46, 1, 8, 37, 106, 161, 94, 1, 9, 50, 187, 426, 485, 190, 1, 10, 65, 302, 937, 1706, 1457, 382, 1, 11, 82, 457, 1814, 4687, 6826, 4373, 766, 1, 12, 101, 658, 3201, 10886, 23437, 27306, 13121, 1534, 1, 13, 122, 911, 5266

Offset: 0

Author

Paul Barry, Dec 09 2003

Keywords

• easy
• nonn
• tabl

Comments

Nodes on a tree with degree k interior nodes and degree 1 boundary nodes.

Examples

			Rows begin:
  1 4 10 22 ...
  1 5 17 53 ...
  1 6 26 106 ...
  1 7 37 187 ...
		

Links

• L. He, X. Liu and G. Strang, Trees with Cantor Eigenvalue Distribution, Studies in Applied Mathematics 110 (2), 123-138, 2003.

Crossrefs

Rows include A033484, A048473, A020989, A057651, A061801, A090843.

Formula

The total number of nodes on a tree with degree k interior nodes and degree 1 boundary nodes is given by N(k, r) = (k*(k-1)^r-2)/(k-2).

G.f.: Sum_{k>=0} (1+x*y)/(1-x*y)/(1-(k+2)*x*y)*y^k. - Vladeta Jovovic, Dec 12 2003