%I
%S 3,7,9,12,16,21,25,32,37
%N Solution to Forest of Numbers (Bosque de NĂºmeros) puzzle for Opaque Rooks 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 and vertically. 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 that a Chess Rook attack in the same row and column 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 Solution for a(5) = 12 from Rodolfo Kurchan:
%e ++++++
%e  1    4  3 
%e ++++++
%e  6     5 
%e ++++++
%e     11 7 
%e ++++++
%e      9 
%e ++++++
%e  8  10 12  2 
%e ++++++
%e Solutions for a(2) to a(6) from Rodolfo Kurchan.
%e Solutions for a(7) to a(10) from Giorgio Vecchi.
%Y Cf. A350627, A352814, A353070, A353093.
%K nonn,more
%O 2,1
%A _Rodolfo Kurchan_, Apr 23 2022
