%I #21 Apr 29 2022 15:53:33
%S 3,5,8,10,13,15,17,19
%N Solution to Forest of Numbers (Bosque de Números) puzzle for Transparent Queens starting with numbers 1 and 2 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 and 2 anywhere. Now place the numbers 3, 4, ..., m in order, subject to the rule that when you place k, the sum of the numbers in the same row, column and diagonal must equal k. Then a(n) is the maximum m that can be achieved.
%H Rodolfo Kurchan, <a href="https://www.puzzlefun.online/problems">Puzzle Fun, Problems, Forest of Numbers</a>
%e Solutions for 5 <= n <= 8 from _Pontus von Brömssen_:
%e +---+---+---+---+---+
%e | 1 | | 2 | 8 | |
%e +---+---+---+---+---+
%e | 9 | 3 | 5 | | |
%e +---+---+---+---+---+
%e | | | | | 6 |
%e +---+---+---+---+---+
%e | |10 | | | |
%e +---+---+---+---+---+
%e | | 7 | | | 4 |
%e +---+---+---+---+---+
%e .
%e +---+---+---+---+---+---+
%e | 1 | 9 | | 8 | | |
%e +---+---+---+---+---+---+
%e | | | | 7 | |12 |
%e +---+---+---+---+---+---+
%e |10 | | | | | |
%e +---+---+---+---+---+---+
%e | | | 6 | | | 2 |
%e +---+---+---+---+---+---+
%e | 5 | | | |11 | |
%e +---+---+---+---+---+---+
%e | 4 | |13 | | | 3 |
%e +---+---+---+---+---+---+
%e .
%e +---+---+---+---+---+---+---+
%e | | 8 | | 6 | | | |
%e +---+---+---+---+---+---+---+
%e | |11 | 2 | | | | |
%e +---+---+---+---+---+---+---+
%e | | | | | 5 | |15 |
%e +---+---+---+---+---+---+---+
%e | 3 | | | 1 | | |10 |
%e +---+---+---+---+---+---+---+
%e |14 | | | | | | |
%e +---+---+---+---+---+---+---+
%e | 7 | |12 | | | | |
%e +---+---+---+---+---+---+---+
%e | 4 | | | | 9 |13 | |
%e +---+---+---+---+---+---+---+
%e .
%e +---+---+---+---+---+---+---+---+
%e | 1 | 3 | |12 | 6 | | 2 | |
%e +---+---+---+---+---+---+---+---+
%e | 4 | | | | | |11 | |
%e +---+---+---+---+---+---+---+---+
%e | | | 7 | |15 | | | |
%e +---+---+---+---+---+---+---+---+
%e | | | | | | | |14 |
%e +---+---+---+---+---+---+---+---+
%e | |13 | | | | | | |
%e +---+---+---+---+---+---+---+---+
%e |10 | | | | | | 5 | |
%e +---+---+---+---+---+---+---+---+
%e | | |16 | | | 9 | | |
%e +---+---+---+---+---+---+---+---+
%e | | | | | |17 | | 8 |
%e +---+---+---+---+---+---+---+---+
%e Solution for a(9) = 19 from Giorgio Vecchi
%Y Cf. A352814, A350627.
%K nonn,more
%O 2,1
%A _Rodolfo Kurchan_, Apr 21 2022