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A114163 Triangle read by rows, based on a simple Jacobsthal number recursion rule. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Subdiagonal S(n+1,n) is A000975(n+1). Row sums of inverse are 0^n.
LINKS
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
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Nov 14 2005
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)