A308881 - OEIS

%I #21 Mar 07 2020 13:50:20

%S 0,0,2,1,3,0,2,1,1,3,4,2,0,5,0,2,1,5,1,3,4,0,2,0,5,1,3,1,2,4,0,2,1,5,

%T 3,1,3,4,0,6,2,0,5,1,7,3,1,2,4,0,4,5,0,3,1,0,2,1,5,3,4,1,3,4,0,7,2,2,

%U 0,5,1,6,9,3,1,2,4,0,5,4,6,0,3,1,7,5,7,8,6,4,10

%N Irregular array read by rows: row k (k>=1) contains k^2 numbers, formed by filling in a k X k square by upwards antidiagonals so entries in all rows, columns, diagonals, antidiagonals are distinct, and then reading that square across rows.

%C The first row of the k X k square converges to A295563 as k increases.

%C When filling in the k X k square, always choose the smallest possible number. Each k X k square is uniquely determined.

%H I. V. Serov, <a href="/A308881/b308881.txt">Rows of first 32 squares, flattened (There are 1^2+2^2+...+32^2 = 11440 entries.)</a>

%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 The first eight squares are (here A=10, B=11, C=12):

%e 0

%e --------

%e 02

%e 13

%e --------

%e 021

%e 134

%e 205

%e --------

%e 0215

%e 1340

%e 2051

%e 3124

%e --------

%e 02153

%e 13406

%e 20517

%e 31240

%e 45031

%e --------

%e 021534

%e 134072

%e 205169

%e 312405

%e 460317

%e 57864A

%e --------

%e 0215349

%e 1340725

%e 2051864

%e 3124058

%e 4603172

%e 5786493

%e 6432587

%e --------

%e 0215349A

%e 13407258

%e 20518643

%e 31240786

%e 4603152B

%e 5786493C

%e 64325879

%e 756893A2

%e --------

%Y Cf. A295563, A308880.

%K nonn,tabf

%O 1,3

%A _N. J. A. Sloane_, Jun 29 2019