

A292675


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 5 X 5 block no symbol occurs twice.


1



1, 4, 9, 16, 25, 27, 29, 32, 33, 33, 33, 34, 35, 35, 35, 36, 37, 38, 40, 40, 40, 40, 40, 40, 40, 40, 41, 43, 42, 42, 46, 47, 48, 52, 53, 53, 54, 57, 58, 58, 59, 62, 63, 64, 66, 68, 70, 72, 73, 74, 75, 75, 78, 78
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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.
In contrast to the sudoku case, the 5 X 5 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 4 (having up to 9*9 = 81 grid points).


LINKS

Table of n, a(n) for n=1..54.
Eric W. Weisstein, Moore Neighborhood, on MathWorldA Wolfram Web Resource.


PROG

(PARI) a(n, m=5, 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, im+1)..i, max(1, jm+1)..min(#g, j+m1)])), 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.


CROSSREFS

Cf. A292670, A292671, A292672, ..., A292679
Sequence in context: A074373 A067115 A061077 * A254719 A266918 A086132
Adjacent sequences: A292672 A292673 A292674 * A292676 A292677 A292678


KEYWORD

nonn,more


AUTHOR

M. F. Hasler, Sep 20 2017


STATUS

approved



