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A292679 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 9 X 9 block no symbol occurs twice.

%I A292679 #13 Feb 16 2025 08:33:51
%S A292679 1,4,9,16,25,36,49,64,81,83,85,88,89,91,92,94,95,95,96,97,100,102,103,
%T A292679 104,103,105,102,103,104,104,104,104,105,107,108,108,115,114,115,111,
%U A292679 112,112,111,113,117,118,119,120,121,122,123,124,126,126,126,126,126,126
%N A292679 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 9 X 9 block no symbol occurs twice.
%C A292679 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 A292679 In contrast to the sudoku case, the 9 X 9 rectangles have "floating" borders, so the constraint is actually equivalent to say that an element must be different from all neighbors in a Moore neighborhood of range 8 (having up to 17*17 = 289 grid points).
%C A292679 See sequences A292672, A292673, A292674 for examples.
%H A292679 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MooreNeighborhood.html">Moore Neighborhood</a>
%o A292679 (PARI) a(n,m=9,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.
%o A292679 (Python) # uses function in A292673
%o A292679 print([A292673(n, b=9) for n in range(1, 101)]) # _Michael S. Branicky_, Apr 13 2023
%Y A292679 Cf. A292670, A292671, A292672, ..., A292678.
%K A292679 nonn
%O A292679 1,2
%A A292679 _M. F. Hasler_, Sep 20 2017