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

1, 9, 17, 26, 37, 47

Offset

1,2

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.

Links

Table of n, a(n) for n=1..6.

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

Formula

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

Example

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

Crossrefs

Cf. A337663.

Sequence in context: A056233 A260264 A126623 * A235361 A109333 A081030

Adjacent sequences: A342431 A342432 A342433 * A342435 A342436 A342437

Keyword

nonn,more,hard

Author

Jeremy Rebenstock and Thomas Ladouceur, Mar 12 2021

Status

approved