cp's OEIS Frontend

A292677 Least number of symbols required to fill a grid of size n X n row by row in the greedy way such that in no row or column or 7 X 7 square any symbol occurs twice.

%I A292677 #19 Feb 16 2025 08:33:51
%S A292677 1,4,9,16,25,36,49,51,53,56,57,59,60,60,61,62,64,66,65,64,62,62,64,66,
%T A292677 65,67,67,67,66,67,69,67,69,69,70,70,73,73,73,73,73,73,73,73,73,73,73,
%U A292677 73,73,73,73,75,76,78,80,80,83,82,83,87,94,99,106,107,108,109,110,111,112,112
%N A292677 Least number of symbols required to fill a grid of size n X n row by row in the greedy way such that in no row or column or 7 X 7 square any symbol occurs twice.
%C A292677 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 A292677 In contrast to the sudoku case, the 7 X 7 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 6 (having up to 13*13 = 169 grid points).
%H A292677 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MooreNeighborhood.html">Moore Neighborhood</a>
%o A292677 (PARI) a(n,m=7,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 A292677 (Python) # uses function in A292673
%o A292677 print([A292673(n, b=7) for n in range(1, 101)]) # _Michael S. Branicky_, Apr 13 2023
%Y A292677 Cf. A292670, A292671, A292672, ..., A292679.
%K A292677 nonn
%O A292677 1,2
%A A292677 _M. F. Hasler_, Sep 20 2017
%E A292677 Terms a(60) and beyond from _Andrew Howroyd_, Feb 22 2020