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

Author

Jan Koornstra, Apr 02 2019

Keywords

• nonn
• fini
• full

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.

Examples

			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.