A364882 a(1)=1 and thereafter a(n) is the number of locations 1..n-1 which are visited last in a single path beginning at some location s, in which one proceeds from location i to i +- a(i) (within 1..n-1) until no further unvisited location is available.

1, 1, 2, 3, 3, 3, 3, 4, 6, 6, 7, 7, 7, 7, 7, 7, 9, 9, 9, 11, 11, 11, 14, 15, 15, 15, 15, 17, 18, 18, 18, 19, 19, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 40, 40

Offset: 1

Author

Neal Gersh Tolunsky, Aug 11 2023

Keywords

• nonn

Comments

A location can be visited no more than once in a single path.

Examples

			a(9)=6 because there are 6 locations which can be visited last (as a dead end) among i=1..8. The 6 locations are i=1,2,3,5,7,8. The following shows a path in which the last location is i=5, beginning at location s=8:
  1 2 3 4 5 6 7 8   location number i
  1,1,2,3,3,3,3,4   a(i)
  1<----3<------4
  1>1>2-->3
From i=5, the only jumps are back to i=1 or forward to i=8, both of which were already visited, so i=5 is one possible dead end term. Here is a path illustrating how i=7 can be a dead end term. We begin at s=4.
  1 2 3 4 5 6 7 8   location number i
  1,1,2,3,3,3,3,4   a(i)
        3---->3
From i=7, we can only jump back to i=4, which was already visited, so i=7 is a dead end term. There are 4 other locations which can be last (or dead ends), for a total of 6 such locations, so a(9)=6.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..246
• Kevin Ryde, C Code

Crossrefs

Cf. A364392, A360744, A360593.

Extensions

More terms from Kevin Ryde, Aug 26 2023