login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292670 Least number of symbols required to fill a grid of size n^2 X n^2 row by row in the greedy way such that in no row or column or n X n square any symbol occurs twice. 9
1, 6, 14, 26, 40, 53, 73, 114 (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 n X n rectangles have "floating" borders, so the constraint is actually equivalent to say that any element must be different from all neighbors in a Moore neighborhood of range n-1 (having up to (2n-1)^2 grid points).

LINKS

Table of n, a(n) for n=1..8.

Eric W. Weisstein, Moore Neighborhood, on MathWorld--A Wolfram Web Resource.

EXAMPLE

For n = 2, the 4 X 4 grid is filled as follows:

   [1 2 3 4]

   [3 4 1 2]

   [2 5 6 3]

   [4 1 2 5], whence a(2) = 6.

PROG

(PARI) a(m, n=m^2, 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^2 X n^2 board.

CROSSREFS

Cf. A292671: grid size independent of block size; A292672, ..., A292679: A(m,n) for fixed n=2,...,9).

Sequence in context: A026055 A288939 A165986 * A131951 A168648 A093776

Adjacent sequences:  A292667 A292668 A292669 * A292671 A292672 A292673

KEYWORD

nonn,more

AUTHOR

M. F. Hasler, Sep 20 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 09:52 EST 2020. Contains 330949 sequences. (Running on oeis4.)