A342434 Solution to stepping stone puzzle on a hexagonal board (See Comments).

1, 9, 17, 26, 37, 47

Offset: 1

Author

Jeremy Rebenstock and Thomas Ladouceur, Mar 12 2021

Keywords

• nonn
• more
• hard

Comments

This is a variant of the stepping stone sequence (A337663), where now the board is a hexagonal grid.

Start with an infinite hexagonal grid. Each cell has six neighbors. Place n 1's anywhere. Now place the numbers 2, 3, ..., m in order, subject to the rule that when you place k, the sum of its neighbors must equal k. Then a(n) is the maximum m that can be achieved.

Examples

			Found by code compiled by Hugo van der Sanden and Thomas Ladouceur, see links titled: "Illustration for a(2)" and "Illustration for a(5)".
		

Links

• Jeremy Rebenstock, Illustration for a(2)
• Jeremy Rebenstock, Illustration for a(5) [Corrected by _Al Zimmermann_, Nov 27 2022]
• Jeremy Rebenstock, Illustration for lower bound

Crossrefs

Cf. A337663.

Formula

a(n) >= 5n - 4. This is seen by constructing the pattern linked above, titled "Illustration for lower bound".