cp's OEIS Frontend

A317191 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).

%I A317191 #31 Mar 07 2020 13:50:20
%S A317191 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 A317191 40,45,33,49,18,17,20,53,16,51,59,18,59,60,58,64,69,69,38,29,74,26,68,
%U A317191 78,80,36,30,33,41,39,32,33,92,41,38,89,32,35
%N A317191 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 A317191 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 A317191 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 A317191 For n=3 the array T is
%e A317191 0 2 1
%e A317191 1 3 4
%e A317191 2 0 5
%e A317191 so a(3) = T(3,3) = 5.
%e A317191 For n=6 the array T is
%e A317191 0 2 1 5 3 4
%e A317191 1 3 4 0 7 2
%e A317191 2 0 5 1 6 9
%e A317191 3 1 2 4 0 5
%e A317191 4 6 0 3 1 7
%e A317191 5 7 8 6 4 10
%e A317191 so a(6) = T(6,6) = 10. This is the first time this sequence differs from A317190.
%Y A317191 Cf. A317190, A274318, A269529, A274528.
%K A317191 nonn
%O A317191 1,2
%A A317191 _N. J. A. Sloane_ and _Doron Zeilberger_, Jul 30 2018