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A292672 Least number of symbols required to fill a grid of size n X n row by row in the greedy way such that in any row or column or rectangular 2 X 2 block no symbol occurs twice. 10

%I

%S 1,4,6,6,7,8,10,10,13,15,16,17,19,20,21,22,23,25,28,30,31,32,33,35,35,

%T 37,38,39,40,41,43,44,45,47,50,52,53,55,57,58,60,60,61,63,64,65,67,68,

%U 70,71,72,73,74,76,78,78,79,80,82,84,85,87,89,90,92,93,94

%N Least number of symbols required to fill a grid of size n X n row by row in the greedy way such that in any row or column or rectangular 2 X 2 block no symbol occurs twice.

%C Consider the symbols as positive integers. By the greedy way we mean to fill the grid row by row from left to right always with the least possible positive integer such that the three constraints (on rows, columns and rectangular blocks) are satisfied.

%C In contrast to the sudoku case, the 2 X 2 rectangles have "floating" borders, so the constraint is actually equivalent to saying that any element must be different from all neighbors in a Moore neighborhood of range 1 (having up to 3*3=9 grid points).

%H Andrew Howroyd, <a href="/A292672/b292672.txt">Table of n, a(n) for n = 1..100</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MooreNeighborhood.html">Moore Neighborhood</a>

%e For n = 4, the 4 X 4 grid is filled as follows:

%e [1 2 3 4]

%e [3 4 1 2]

%e [2 5 6 3]

%e [4 1 2 5], whence a(4) = 6.

%e For n = 3 the result would be the upper 3 X 3 part of the above grid, showing that also a(3) = 6.

%o (PARI) a(n,m=2,g=matrix(n,n))={my(ok(g,k,i,j,m)=if(m,ok(g[i,],k)&&ok(g[,j],k)&&ok(concat(Vec(g[max(1,i-m+1)..i,max(1,j-m+1)..min(#g,j+m-1)])),k),!setsearch(Set(g),k))); for(i=1,n,for(j=1,n,for(k=1,n^2,ok(g,k,i,j,m)&&(g[i,j]=k)&&break)));vecmax(g)} \\ without "vecmax" the program returns the full n X n board.

%Y Cf. A292670, A292671, A292673, ..., A292679.

%K nonn

%O 1,2

%A _M. F. Hasler_, Sep 20 2017

%E Terms a(60) and beyond from _Andrew Howroyd_, Feb 22 2020

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Last modified September 22 15:04 EDT 2021. Contains 347607 sequences. (Running on oeis4.)