cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A362016 Maximal number of unmarked cells with at least 3 marked neighboring cells in the n X n kings' graph.

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%I A362016 #18 Aug 24 2023 09:43:37
%S A362016 0,1,4,8,13,20,28,38,50,61,75,90,108,124,139
%N A362016 Maximal number of unmarked cells with at least 3 marked neighboring cells in the n X n kings' graph.
%C A362016 The value of r = lim sup a(n) / n^2 is in the half-open interval [2/3, 8/11).
%C A362016 It appears from the computed terms that r = 2/3.
%H A362016 Tomas Rigaux, <a href="/A362016/a362016.py.txt">Python program</a>
%e A362016 a(2) = 1, as the only pattern is
%e A362016   .X
%e A362016   XX
%e A362016 a(9) = 50, with a similar pattern to prove that r >= 2/3:
%e A362016   X.......X
%e A362016   .XXXXXXX.
%e A362016   X.......X
%e A362016   .........
%e A362016   XXXXXXXXX
%e A362016   .........
%e A362016   X.......X
%e A362016   .XXXXXXX.
%e A362016   X.......X
%e A362016 a(10) = 61, and a pattern that reaches that is
%e A362016   X..X...X..
%e A362016   XX.X.X.X.X
%e A362016   ..........
%e A362016   .X.XX.X.XX
%e A362016   XX....X...
%e A362016   ....X....X
%e A362016   X.XX..XX.X
%e A362016   X....X....
%e A362016   ...X....XX
%e A362016   XX.X.XX.X.
%Y A362016 If we only want 1 marked neighbor, we get n^2 - A075561(n).
%K A362016 nonn,hard,more
%O A362016 1,3
%A A362016 _Tomas Rigaux_, Apr 04 2023