A317191 - OEIS

%I #31 Mar 07 2020 13:50:20

%S 0,3,5,4,1,10,7,2,6,8,15,12,19,17,22,23,12,26,11,31,32,12,35,10,37,42,

%T 40,45,33,49,18,17,20,53,16,51,59,18,59,60,58,64,69,69,38,29,74,26,68,

%U 78,80,36,30,33,41,39,32,33,92,41,38,89,32,35

%N Fill an n X n square array T(j,k), 1<=j<=n, 1=k<=n, by antidiagonals upwards in which each term is the least nonnegative integer satisfying the condition that no row, column, diagonal, or antidiagonal contains a repeated term; a(n) = T(n,n).

%C This is the analog for an n X n board of the sequence A317190 (which is the main diagonal when we fill in the whole of the fourth quadrant in this way).

%H F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, <a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i1p52/8039">Queens in exile: non-attacking queens on infinite chess boards</a>, Electronic J. Combin., 27:1 (2020), #P1.52.

%e For n=3 the array T is

%e 0 2 1

%e 1 3 4

%e 2 0 5

%e so a(3) = T(3,3) = 5.

%e For n=6 the array T is

%e 0 2 1 5 3 4

%e 1 3 4 0 7 2

%e 2 0 5 1 6 9

%e 3 1 2 4 0 5

%e 4 6 0 3 1 7

%e 5 7 8 6 4 10

%e so a(6) = T(6,6) = 10. This is the first time this sequence differs from A317190.

%Y Cf. A317190, A274318, A269529, A274528.

%K nonn

%O 1,2

%A _N. J. A. Sloane_ and _Doron Zeilberger_, Jul 30 2018