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A353070 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).

%I A353070 #21 Apr 29 2022 15:53:33
%S A353070 3,5,8,10,13,15,17,19
%N A353070 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 A353070 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 A353070 Rodolfo Kurchan, <a href="https://www.puzzlefun.online/problems">Puzzle Fun, Problems, Forest of Numbers</a>
%e A353070 Solutions for 5 <= n <= 8 from _Pontus von Brömssen_:
%e A353070   +---+---+---+---+---+
%e A353070   | 1 |   | 2 | 8 |   |
%e A353070   +---+---+---+---+---+
%e A353070   | 9 | 3 | 5 |   |   |
%e A353070   +---+---+---+---+---+
%e A353070   |   |   |   |   | 6 |
%e A353070   +---+---+---+---+---+
%e A353070   |   |10 |   |   |   |
%e A353070   +---+---+---+---+---+
%e A353070   |   | 7 |   |   | 4 |
%e A353070   +---+---+---+---+---+
%e A353070 .
%e A353070   +---+---+---+---+---+---+
%e A353070   | 1 | 9 |   | 8 |   |   |
%e A353070   +---+---+---+---+---+---+
%e A353070   |   |   |   | 7 |   |12 |
%e A353070   +---+---+---+---+---+---+
%e A353070   |10 |   |   |   |   |   |
%e A353070   +---+---+---+---+---+---+
%e A353070   |   |   | 6 |   |   | 2 |
%e A353070   +---+---+---+---+---+---+
%e A353070   | 5 |   |   |   |11 |   |
%e A353070   +---+---+---+---+---+---+
%e A353070   | 4 |   |13 |   |   | 3 |
%e A353070   +---+---+---+---+---+---+
%e A353070 .
%e A353070   +---+---+---+---+---+---+---+
%e A353070   |   | 8 |   | 6 |   |   |   |
%e A353070   +---+---+---+---+---+---+---+
%e A353070   |   |11 | 2 |   |   |   |   |
%e A353070   +---+---+---+---+---+---+---+
%e A353070   |   |   |   |   | 5 |   |15 |
%e A353070   +---+---+---+---+---+---+---+
%e A353070   | 3 |   |   | 1 |   |   |10 |
%e A353070   +---+---+---+---+---+---+---+
%e A353070   |14 |   |   |   |   |   |   |
%e A353070   +---+---+---+---+---+---+---+
%e A353070   | 7 |   |12 |   |   |   |   |
%e A353070   +---+---+---+---+---+---+---+
%e A353070   | 4 |   |   |   | 9 |13 |   |
%e A353070   +---+---+---+---+---+---+---+
%e A353070 .
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070   | 1 | 3 |   |12 | 6 |   | 2 |   |
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070   | 4 |   |   |   |   |   |11 |   |
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070   |   |   | 7 |   |15 |   |   |   |
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070   |   |   |   |   |   |   |   |14 |
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070   |   |13 |   |   |   |   |   |   |
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070   |10 |   |   |   |   |   | 5 |   |
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070   |   |   |16 |   |   | 9 |   |   |
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070   |   |   |   |   |   |17 |   | 8 |
%e A353070   +---+---+---+---+---+---+---+---+
%e A353070 Solution for a(9) = 19 from Giorgio Vecchi
%Y A353070 Cf. A352814, A350627.
%K A353070 nonn,more
%O A353070 2,1
%A A353070 _Rodolfo Kurchan_, Apr 21 2022