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%I A329094 #9 Sep 11 2021 19:28:10
%S A329094 1,1,1,1,1,3,3,8,17,18,51,69,126,286,485,1180,2245,4312,7247,19559,
%T A329094 41403,66454,161131,337495,710899,1286527,3069554,7100614,15046664,
%U A329094 29090692,57797782,144576706,313441617,628544270,1278592587,3304149943,7192582862
%N A329094 a(n) is the number of solutions when placing the numbers 1..n in an n X n square according to the rules in the Comments section.
%C A329094 Place a 1 in the upper left corner of the square. Let k be the number placed last. At each step place k+1 at a distance k vertically or horizontally from k. Solutions are counted up to mirroring in the backward diagonal. That is, all solutions have 2 to the right of 1. Obviously, n is the largest possible value since the next step will inevitably lead outside the square.
%e A329094 Sample solutions:
%e A329094   n=6                  n=7                     n=8
%e A329094   1  2  -  -  -  -     1  2  -  -  -  -  -     1  2  -  -  -  -  8  -
%e A329094   -  -  -  -  -  -     7  5  -  -  -  -  6     -  -  -  -  -  -  -  -
%e A329094   -  3  -  -  -  -     -  3  -  -  -  -  -     5  3  -  -  4  -  -  -
%e A329094   -  -  -  -  -  -     -  -  -  -  -  -  -     -  -  -  -  -  -  -  -
%e A329094   -  -  -  -  -  -     -  -  -  -  -  -  -     -  -  -  -  -  -  -  -
%e A329094   6  4  -  -  -  5     -  4  -  -  -  -  -     -  -  -  -  -  -  -  -
%e A329094                        -  -  -  -  -  -  -     -  -  -  -  -  -  -  -
%e A329094                                                6  -  -  -  -  -  7  -
%Y A329094 Cf. A308353.
%K A329094 nonn
%O A329094 1,6
%A A329094 _Lars Blomberg_, Nov 04 2019

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