%I
%S 1,3,8,12,19,25,34
%N 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 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 Rudolfo Kurchan, <a href="http://www.puzzlefun.online">Puzzle Fun</a>
%e 4 X 4 solution with m = a(4) = 12 from Hector San Segundo:
%e +++++
%e   10 3  8 
%e +++++
%e   6 1 4
%e +++++
%e   2  5
%e +++++
%e  11 9 7 12
%e +++++
%e 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 5 X 5 solution with m = a(5) = 19 from _Pontus von Brömssen_:
%e ++++++
%e  5 6 7 8 18
%e ++++++
%e  11  1  10
%e ++++++
%e  14  19 2 16
%e ++++++
%e   3 9 4 
%e ++++++
%e  15 12  13 17
%e ++++++
%e .
%e 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 +++++++
%e  22 1 15 19  20
%e +++++++
%e  7 14   4 16
%e +++++++
%e   6  21  12
%e +++++++
%e  17  9  8 25
%e +++++++
%e   11  3 5 
%e +++++++
%e  24 13 2 10 18 23
%e +++++++
%e .
%e a(7) = 34 from Giorgio Vecchi.
%Y Cf. A350627.
%K nonn,more
%O 1,2
%A _Rodolfo Kurchan_, Apr 04 2022
%E a(6) corrected by _Pontus von Brömssen_, Apr 15 2022
