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A308178 Scan an infinite 45-degree triangular chessboard (cells (x,y) with 0 <= y <= x) by upwards antidiagonals, filling in each cell with the smallest nonnegative number already placed that cannot be seen by a chess queen at (x,y); sequence gives numbers along the successive antidiagonals.

%I A308178 #27 May 30 2019 16:49:52
%S A308178 0,1,2,3,3,0,4,1,5,5,2,4,6,7,0,2,7,4,1,3,8,5,2,4,1,9,6,3,0,2,10,11,7,
%T A308178 1,3,6,11,8,10,9,4,5,12,9,6,8,0,10,7,13,10,12,5,6,11,8,14,15,8,7,9,3,
%U A308178 5,11,15,12,9,6,8,0,13,10,16,13,11,12,5,1,14,7
%N A308178 Scan an infinite 45-degree triangular chessboard (cells (x,y) with 0 <= y <= x) by upwards antidiagonals, filling in each cell with the smallest nonnegative number already placed that cannot be seen by a chess queen at (x,y); sequence gives numbers along the successive antidiagonals.
%C A308178 The 0's occur in positions (x,y) = (2k,k), k >= 0.
%C A308178 Column y=1 is A263313; the main diagonal is A308180.
%C A308178 After 13 steps, the y=2 column appears to become quasi-periodic with a saltus of 4. That is, the first differences appear to become periodic with period (-1, -2, 1, 6).
%C A308178 There is a very similar triangle in A274650.
%H A308178 Rémy Sigrist, <a href="/A308178/b308178.txt">Table of n, a(n) for n = 0..10200</a> (antidiagonals for x+y = 0..200)
%H A308178 Rémy Sigrist, <a href="/A308178/a308178.png">Colored representation of the first 1000 antidiagonals</a> (black pixels correspond to zeros)
%H A308178 Rémy Sigrist, <a href="/A308178/a308178.gp.txt">PARI program for A308178</a>
%e A308178 Start of chessboard showing antidiagonals 0 through 12:
%e A308178 y =  0, 1, 2, 3, 4, 5, 6, 7, ...
%e A308178 --------------------------------
%e A308178 x=0  0,
%e A308178 x=1  1, 3,
%e A308178 x=2  2, 0, 5,
%e A308178 x=3  3, 1, 4, 2,
%e A308178 x=4  4, 2, 0, 3, 1,
%e A308178 x=5  5, 7, 1, 4, 2, 6,
%e A308178 x=6  6, 4, 2, 0, 3, 5, 7,
%e A308178 x=7  7, 5, 3, 1, 4, 10, ...,
%e A308178 x=8  8, 6, 7, 9, 0, ...,
%e A308178 x=9  9, 11, 10, 8, ...,
%e A308178 x=10 10, 8, 6, ...,
%e A308178 x=11 11, 9, ...,
%e A308178 x=12 12, ...,
%e A308178 x=13 ...,
%e A308178 The first few antidiagonals are:
%e A308178 0,
%e A308178 1,
%e A308178 2, 3,
%e A308178 3, 0,
%e A308178 4, 1, 5,
%e A308178 5, 2, 4,
%e A308178 6, 7, 0, 2,
%e A308178 7, 4, 1, 3,
%e A308178 8, 5, 2, 4, 1,
%e A308178 9, 6, 3, 0, 2,
%e A308178 ...
%o A308178 (PARI) See Links section.
%Y A308178 Reading the triangle across rows gives A308179.
%Y A308178 Cf. A263313, A274650, A308180
%K A308178 nonn,tabf
%O A308178 0,3
%A A308178 _N. J. A. Sloane_, May 28 2019
%E A308178 More terms from _Rémy Sigrist_, May 29 2019