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A352814 Solution to Forest of Numbers (Bosque de Números) puzzle if we start with the numbers 1 through n for an n X n square grid (see Comments).

%I A352814 #15 Apr 16 2022 03:15:03
%S A352814 1,3,8,12,19,25,34
%N A352814 Solution to Forest of Numbers (Bosque de Números) puzzle if we start with the numbers 1 through n for an n X n square grid (see Comments).
%C A352814 Start with an n X n square grid. Each cell has neighbors horizontally, vertically and diagonally. Place the numbers 1 to n anywhere. Now place the numbers n+1, n+2, ..., 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 A352814 Rudolfo Kurchan, <a href="http://www.puzzlefun.online">Puzzle Fun</a>
%e A352814 4 X 4 solution with m = a(4) = 12 from Hector San Segundo:
%e A352814   +---+---+---+---+
%e A352814   |   | 10| 3 | 8 |
%e A352814   +---+---+---+---+
%e A352814   |   |  6|  1|  4|
%e A352814   +---+---+---+---+
%e A352814   |   |  2|   |  5|
%e A352814   +---+---+---+---+
%e A352814   | 11|  9|  7| 12|
%e A352814   +---+---+---+---+
%e A352814 4 = 1 + 3, 5 = 1 + 4, 6 = 1 + 2 + 3, 7 = 2 + 5, 8 = 1 + 3 + 4, 9 = 2 + 7, 10 = 1 + 3 + 6, 11 = 2 + 9, 12 = 5 + 7.
%e A352814 5 X 5 solution with m = a(5) = 19 from _Pontus von Brömssen_:
%e A352814   +---+---+---+---+---+
%e A352814   |  5|  6|  7|  8| 18|
%e A352814   +---+---+---+---+---+
%e A352814   | 11|   |  1|   | 10|
%e A352814   +---+---+---+---+---+
%e A352814   | 14|   | 19|  2| 16|
%e A352814   +---+---+---+---+---+
%e A352814   |   |  3|  9|  4|   |
%e A352814   +---+---+---+---+---+
%e A352814   | 15| 12|   | 13| 17|
%e A352814   +---+---+---+---+---+
%e A352814 .
%e A352814 One of 10 6 X 6 solutions (up to rotations and reflections) with m = a(6) = 25 from _Pontus von Brömssen_, Apr 15 2022:
%e A352814   +---+---+---+---+---+---+
%e A352814   | 22|  1| 15| 19|   | 20|
%e A352814   +---+---+---+---+---+---+
%e A352814   |  7| 14|   |   |  4| 16|
%e A352814   +---+---+---+---+---+---+
%e A352814   |   |  6|   | 21|   | 12|
%e A352814   +---+---+---+---+---+---+
%e A352814   | 17|   |  9|   |  8| 25|
%e A352814   +---+---+---+---+---+---+
%e A352814   |   | 11|   |  3|  5|   |
%e A352814   +---+---+---+---+---+---+
%e A352814   | 24| 13|  2| 10| 18| 23|
%e A352814   +---+---+---+---+---+---+
%e A352814 .
%e A352814 a(7) = 34 from Giorgio Vecchi.
%Y A352814 Cf. A350627.
%K A352814 nonn,more
%O A352814 1,2
%A A352814 _Rodolfo Kurchan_, Apr 04 2022
%E A352814 a(6) corrected by _Pontus von Brömssen_, Apr 15 2022