A114163 Triangle read by rows, based on a simple Jacobsthal number recursion rule.

1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 18, 10, 1, 1, 5, 58, 68, 21, 1, 1, 6, 179, 398, 299, 42, 1, 1, 7, 543, 2169, 3687, 1181, 85, 1, 1, 8, 1636, 11388, 42726, 28488, 4836, 170, 1, 1, 9, 4916, 58576, 481374, 640974, 236436, 19286, 341, 1, 1, 10, 14757, 297796, 5353690

Offset: 0

Author

Paul Barry, Nov 14 2005

Keywords

• easy
• nonn
• tabl

Comments

Subdiagonal S(n+1,n) is A000975(n+1). Row sums of inverse are 0^n.

Examples

			Triangle begins
1....1....3....5...11...21...43....J(k+1)
1
1....1
1....2....1
1....3....5....1
1....4...18...10....1
1....5...58...68...21....1
1....6..179..398..299...42....1
For example, T(6,3)=398=58+5*68=T(5,2)+J(4)*T(5,3).
		

Crossrefs

Cf. A111669.

Formula

Number triangle T(n, k)=T(n-1, k-1)+J(k+1)*T(n-1, k) where J(n)=A001045(n); Column k has g.f. x^k/Product(1-J(i+1)x, i, 0, k).