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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. 2
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, 79, 80, 82, 83, 85, 86, 88, 91, 92, 97, 96, 98 (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

Andrew Howroyd, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Moore Neighborhood

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, 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.

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

AUTHOR

M. F. Hasler, Sep 20 2017

EXTENSIONS

Terms a(55) and beyond from Andrew Howroyd, Feb 22 2020

STATUS

approved

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Last modified September 21 19:55 EDT 2021. Contains 347598 sequences. (Running on oeis4.)