A292676 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 6 X 6 block no symbol occurs twice.

1, 4, 9, 16, 25, 36, 38, 38, 40, 40, 41, 41, 43, 45, 48, 48, 50, 49, 49, 49, 49, 50, 50, 51, 51, 52, 51, 52, 53, 53, 53, 53, 53, 53, 55, 53, 55, 55, 59, 59, 59, 61, 65, 64, 66, 70, 68, 69, 72, 73, 78, 78, 79, 84, 85, 85, 86, 90, 90, 90, 94, 93, 96, 97, 99, 102, 105, 106, 106, 107

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 6 X 6 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 5 (having up to 11*11 = 121 grid points).

Links

Table of n, a(n) for n=1..70.

Eric Weisstein's World of Mathematics, Moore Neighborhood

Prog

(PARI) a(n, m=6, 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.
(Python) # uses function in A292673
print([A292673(n, b=6) for n in range(1, 101)]) # Michael S. Branicky, Apr 13 2023

Crossrefs

Cf. A292670, A292671, A292672, ..., A292679

Sequence in context: A070461 A070460 A070459 * A241971 A335640 A302053

Adjacent sequences: A292673 A292674 A292675 * A292677 A292678 A292679

Keyword

nonn

Author

M. F. Hasler, Sep 20 2017

Extensions

Terms a(60) and beyond from Andrew Howroyd, Feb 22 2020

Status

approved