A307344 Cells visited by a single pawn move for an even cell and a double pawn move for an odd cell on a numbered 3D grid and moving to the lowest available unvisited cell of different parity at each step.

1, 10, 19, 48, 27, 76, 51, 20, 33, 8, 15, 4, 9, 34, 53, 108, 77, 28, 13, 2, 5, 30, 47, 18, 31, 6, 3, 12, 23, 72, 49, 102, 71, 22, 11, 36, 21, 70, 101, 186, 131, 252, 193, 106, 75, 26, 43, 16

Offset

1,2

Comments

The grid is numbered as follows:

1: [0, 0, 0]

-- 1 step --

2: [0, 0, 1]

3: [0, 1, 0]

4: [1, 0, 0]

-- 2 steps --

5: [0, 0, 2]

6: [0, 1, 1]

7: [0, 2, 0]

8: [1, 0, 1]

9: [1, 1, 0]

10: [2, 0, 0]

etc.

Links

Table of n, a(n) for n=1..48.

Example

1: [0, 0, 0] is an odd cell, hence a double move is required. Since 5: [0, 0, 2] and 7: [0, 2, 0] are also odd, 10: [2, 0, 0] is the only valid move.
The sequence ends at 16: [1, 1, 1]. A single move is required, which limits the possible destination cells to:
   6: [0, 1, 1], even;
   8: [1, 0, 1], even;
   9: [1, 1, 0], already visited;
  27: [1, 1, 2], already visited;
  28: [1, 2, 1], even;
  31: [2, 1, 1], already visited;

Crossrefs

Cf. A324273, A324274, A324275.

Sequence in context: A082659 A088409 A219959 * A330570 A369305 A065198

Adjacent sequences: A307341 A307342 A307343 * A307345 A307346 A307347

Keyword

nonn,fini,full

Author

Jan Koornstra, Apr 02 2019

Status

approved