OFFSET
1,1
COMMENTS
If two locations j and k can reach other, then they belong to the same strongly connected component and can reach the same set of locations.
a(n) <= a(n-1) + 1.
LINKS
Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
EXAMPLE
a(5)=3 because there are 3 distinct sets of locations which represent the indices reachable from a given location s.
Starting at s=1, we can visit the set of locations i = {1, 3}
1 2 3 4
2, 1, 2, 2
2---->2
This is the same set of locations that can be visited from s=3. Since it is the same set, we only count it once:
1 2 3 4
2, 1, 2, 2
2<----2
From s=2, we can visit the set of locations i = {1, 2, 3}:
1 2 3 4
2, 1, 2, 2
2<-1->2
From s=4, we can visit another distinct set of locations i = {1, 2, 3, 4}
1 2 3 4
2, 1, 2, 2
1<----2
2<-1->2
This gives a total of 3 distinct sets of locations reachable from any starting index (equivalent to 3 strongly connected components):
i = {1, 3}; i = {1, 2, 3}; and i = {1, 2, 3, 4}.
CROSSREFS
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Sep 09 2023
STATUS
approved