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.

1, 4, 9, 16, 25, 36, 49, 51, 53, 56, 57, 59, 60, 60, 61, 62, 64, 66, 65, 64, 62, 62, 64, 66, 65, 67, 67, 67, 66, 67, 69, 67, 69, 69, 70, 70, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 75, 76, 78, 80, 80, 83, 82, 83, 87, 94, 99, 106, 107, 108, 109, 110, 111, 112, 112

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 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).

Links

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

Eric Weisstein's World of Mathematics, Moore Neighborhood

Prog

(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.
(Python) # uses function in A292673
print([A292673(n, b=7) for n in range(1, 101)]) # Michael S. Branicky, Apr 13 2023

Crossrefs

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

Sequence in context: A343066 A028907 A361265 * A292678 A072595 A376172

Adjacent sequences: A292674 A292675 A292676 * A292678 A292679 A292680

Keyword

nonn

Author

M. F. Hasler, Sep 20 2017

Extensions

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

Status

approved