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%I #19 Dec 15 2022 14:09:53
%S 1,9,17,26,37,47
%N Solution to stepping stone puzzle on a hexagonal board (See Comments).
%C This is a variant of the stepping stone sequence (A337663), where now the board is a hexagonal grid.
%C 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.
%H Jeremy Rebenstock, <a href="/A342434/a342434.png">Illustration for a(2)</a>
%H Jeremy Rebenstock, <a href="/A342434/a342434_3.png">Illustration for a(5)</a> [Corrected by _Al Zimmermann_, Nov 27 2022]
%H Jeremy Rebenstock, <a href="/A342434/a342434_2.png">Illustration for lower bound</a>
%F a(n) >= 5n - 4. This is seen by constructing the pattern linked above, titled "Illustration for lower bound".
%e Found by code compiled by Hugo van der Sanden and Thomas Ladouceur, see links titled: "Illustration for a(2)" and "Illustration for a(5)".
%Y Cf. A337663.
%K nonn,more,hard
%O 1,2
%A _Jeremy Rebenstock_ and _Thomas Ladouceur_, Mar 12 2021