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A275897 Read the infinite chessboard underlying A065188 by successive antidiagonals and record when the queens are encountered. Here the rows and columns are indexed starting at 0 (as in A275895).

%I A275897 #26 Mar 07 2020 13:50:20
%S A275897 0,7,13,23,32,96,114,142,163,183,197,261,290,446,484,581,608,795,845,
%T A275897 919,972,1018,1052,1194,1255,1464,1561,1733,1807,1914,1992,2104,2320,
%U A275897 2387,2583,2955,3051,3289,3352,3602,3708,3971,4039,4313,4429,4522,4596,5088,5316,5605,5844,6173,6371
%N A275897 Read the infinite chessboard underlying A065188 by successive antidiagonals and record when the queens are encountered. Here the rows and columns are indexed starting at 0 (as in A275895).
%H A275897 Alois P. Heinz, <a href="/A275897/b275897.txt">Table of n, a(n) for n = 1..10000</a>
%H A275897 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 A275897 The second queen appears in the fourth antidiagonal at position 7 (calling the top left square square 0):
%e A275897 Qxxx
%e A275897 xxxQ
%e A275897 xQxx
%e A275897 xxxx
%e A275897 so a(2) = 7.
%p A275897 # Let b8 be a list of the terms of A065188.
%p A275897 ts:=[];
%p A275897 for n from 1 to 130 do
%p A275897 ta:=b8[n];
%p A275897 tb:=n-1+(ta+n-2)*(ta+n-1)/2;
%p A275897 ts:=[op(ts),tb]; od:
%p A275897 tt:=sort(ts); # A275897
%p A275897 tu:=map(x->x+1,tt); # A275898
%t A275897 b8 = Cases[Import["https://oeis.org/A065188/b065188.txt", "Table"], {_, _}][[All, 2]];
%t A275897 ts = {};
%t A275897 For[n = 1, n <= 130, n++, ta = b8[[n]]; tb = n - 1 + (ta + n - 2)*(ta + n - 1)/2; ts = Append[ts, tb]];
%t A275897 Sort[ts] (* _Jean-François Alcover_, Feb 27 2020, from Maple *)
%Y A275897 Cf. A065188, A275895, A275898.
%K A275897 nonn
%O A275897 1,2
%A A275897 _N. J. A. Sloane_, Aug 23 2016, following a suggestion from _David A. Corneth_