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 A308880 Irregular array read by rows: row k (k>=1) contains k^2 numbers, formed by filling in a k X k square by rows so entries in all rows, columns, diagonals, antidiagonals are distinct, and then reading that square across rows. 2
 0, 0, 1, 2, 3, 0, 1, 2, 2, 3, 0, 1, 4, 5, 0, 1, 2, 3, 2, 3, 0, 1, 1, 4, 5, 2, 5, 0, 1, 4, 0, 1, 2, 3, 4, 2, 3, 0, 1, 5, 1, 4, 5, 2, 0, 5, 0, 1, 4, 3, 3, 6, 7, 0, 1, 0, 1, 2, 3, 4, 5, 2, 3, 0, 1, 6, 7, 1, 4, 5, 2, 0, 8, 5, 0, 1, 4, 3, 6, 3, 7, 6, 0, 1, 4, 4, 2, 9, 5, 7, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The second row of the k X k square converges to A004443 as k increases. When filling in the k X k square, always choose the smallest possible number. Each k X k square is uniquely determined. Each k X k square read downwards by antidiagonals up to and including the main antidiagonal is A274528(1..k*(k+1)/2). - I. V. Serov, Jun 30 2019, following an argument by Bernard Schott. LINKS I. V. Serov, Rows of first 32 squares, flattened (There are 1^2+2^2+...+32^2 = 11440 entries.) 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 first eight squares are (here A=10, B=11, C=12): 0 -------- 01 23 -------- 012 230 145 -------- 0123 2301 1452 5014 -------- 01234 23015 14520 50143 36701 -------- 012345 230167 145208 501436 376014 42957A -------- 0123456 2301674 1452083 5014362 3780145 4265798 9548237 -------- 01234567 23016745 14520836 50143628 37801459 42675983 9548237A A836BC92 -------- Concatenating the rows of these squares gives the sequence. PROG (MATLAB) A308880 = []; A308881 = []; for n = 1:oo; M = [0:(n-1)      zeros(n-1, n-0)*NaN]; for i = 2:n; for j = 1:n; M = Mnext(M, n, i, j); end; end A308880 = [A308880 reshape(M', 1, n^2)]; A308881 = [A308881 reshape(M , 1, n^2)]; end function [M] = Mnext(M, n, i, j); row = M(i, 1:j-1); col = M(1:i-1, j); dim = diag(       M, j-i); dia = diag(fliplr(M), n-i-j+1); X = ([row col' dim' dia']); for m = 0:length(X)-1; if isempty(find(X==m)); break; end; end; M(i, j) = m; end % I. V. Serov, Jun 30 2019 CROSSREFS Cf. A004443, A308881, A274528. Sequence in context: A308898 A106728 A292603 * A319047 A276335 A189480 Adjacent sequences:  A308877 A308878 A308879 * A308881 A308882 A308883 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Jun 29 2019 STATUS approved

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Last modified January 26 06:00 EST 2021. Contains 340434 sequences. (Running on oeis4.)