A275897 - OEIS

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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).

0, 7, 13, 23, 32, 96, 114, 142, 163, 183, 197, 261, 290, 446, 484, 581, 608, 795, 845, 919, 972, 1018, 1052, 1194, 1255, 1464, 1561, 1733, 1807, 1914, 1992, 2104, 2320, 2387, 2583, 2955, 3051, 3289, 3352, 3602, 3708, 3971, 4039, 4313, 4429, 4522, 4596, 5088, 5316, 5605, 5844, 6173, 6371

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

EXAMPLE

The second queen appears in the fourth antidiagonal at position 7 (calling the top left square square 0):

Qxxx

xxxQ

xQxx

xxxx

so a(2) = 7.

MAPLE

# Let b8 be a list of the terms of A065188.

ts:=[];

for n from 1 to 130 do

ta:=b8[n];

tb:=n-1+(ta+n-2)*(ta+n-1)/2;

ts:=[op(ts), tb]; od:

tt:=sort(ts); # A275897

tu:=map(x->x+1, tt); # A275898

MATHEMATICA

b8 = Cases[Import["https://oeis.org/A065188/b065188.txt", "Table"], {_, _}][[All, 2]];

ts = {};

For[n = 1, n <= 130, n++, ta = b8[[n]]; tb = n - 1 + (ta + n - 2)*(ta + n - 1)/2; ts = Append[ts, tb]];

Sort[ts] (* Jean-François Alcover, Feb 27 2020, from Maple *)

CROSSREFS

Cf. A065188, A275895, A275898.

Sequence in context: A147812 A043884 A129727 * A227786 A339148 A270792

Adjacent sequences: A275894 A275895 A275896 * A275898 A275899 A275900

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 23 2016, following a suggestion from David A. Corneth

STATUS

approved