A075529 Let x(0),...,x(n), be an additive chain of length n+1 with x(0)=1 and satisfying x(k) = x(k-1) + x(j) for some j < k. a(n) is the number of distinct possible values taken on by x(n).

1, 1, 2, 4, 8, 16, 30, 55, 98, 175, 310, 555, 986, 1757, 3138, 5618

Offset: 0

Author

Eli Ben-Naim (ebn(AT)lanl.gov), Sep 19 2002

Keywords

• nonn
• more

Examples

			Let X(n) denote the set of possible values for x(n), then X(0) = {1} hence a(0) = 1, X(1) = {2} hence a(1)=1, X(2) = {3,4} hence a(2)=2, X(3) = {4,5,6,8} hence a(3)=4.
		

Links

• E. Ben-Naim and P. L. Krapivsky, Growth and Structure of Stochastic Sequences, J. Phys. A (2002).
• E. Ben-Naim, Home page
• Sean A. Irvine, Java program (github)

Extensions

Entry revised by Sean A. Irvine, Feb 20 2025