A364882 - OEIS

%I #30 Aug 27 2023 04:37:13

%S 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,

%T 18,18,19,19,25,25,25,25,26,26,26,26,26,27,27,27,28,28,28,28,29,29,29,

%U 29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,40,40

%N 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.

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

%H Kevin Ryde, <a href="/A364882/b364882.txt">Table of n, a(n) for n = 1..246</a>

%H Kevin Ryde, <a href="/A364882/a364882.c.txt">C Code</a>

%e 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:

%e   1 2 3 4 5 6 7 8   location number i

%e   1,1,2,3,3,3,3,4   a(i)

%e   1<----3<------4

%e   1>1>2-->3

%e 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.

%e   1 2 3 4 5 6 7 8   location number i

%e   1,1,2,3,3,3,3,4   a(i)

%e         3---->3

%e 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.

%Y Cf. A364392, A360744, A360593.

%K nonn

%O 1,3

%A _Neal Gersh Tolunsky_, Aug 11 2023

%E More terms from _Kevin Ryde_, Aug 26 2023