[seqfan] A002251 rediscovered as "home-sick queens"

wouter meeussen wouter.meeussen at pandora.be
Wed Nov 2 11:09:10 CET 2011


A graphical analogue is sometimes nice to explain an otherwise dull (?) sequence.

On a large chessboard, place a queen in the upper-left corner at (0,0);
then add non-attacking queens as close as possible to the origin.
You get
{0, 0}, {1, 2}, {2, 1}, {3, 5}, {4, 7}, {5, 3}, {6, 10}, {7, 4}, {8, 13}, {9, 15},
 {10, 6}, {11, 18}, {12, 20}, {13, 8}, {14, 23}, {15, 9}, {16, 26}, {17, 28}, {18, 11} etc
The row-index is simply increasing,
the column index is A002251:
"Start with sequence of nonnegative integers; then swap L(k) and U(k) for all k >= 1, 
where L = A000201, U = A001950 (lower and upper Wythoff sequences)."

Isn't this correct?

Wouter.

inspired by http://www.physicsforums.com/showthread.php?p=3590295&posted=1#post3590295
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Mma 4.0 implementation (lazy programmer's)
In[1]:=<<DiscreteMath`Combinatorica`
In[2]:=base=Outer[List,Range[0,64],Range[0,2*64]];
In[3]:=Backtrack[base,(And[UnsameQ@@First /@#,UnsameQ@@Last/@#,UnsameQ@@Subtract@@@#])&,True&,One]
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