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

0,5

Comments

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

Links

Table of n, a(n) for n=0..59.

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).

Example

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.

Sequence in context: A320031 A123349 A123352 * A189435 A279636 A290569

Adjacent sequences: A114160 A114161 A114162 * A114164 A114165 A114166

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 14 2005

Status

approved