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

0,3

Links

Table of n, a(n) for n=0..15.

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)

Example

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.

Crossrefs

Sequence in context: A271480 A226454 A347775 * A005305 A298402 A125548

Adjacent sequences: A075526 A075527 A075528 * A075530 A075531 A075532

Keyword

nonn,more,changed

Author

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

Extensions

Entry revised by Sean A. Irvine, Feb 20 2025

Status

approved