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A199134
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Indices of Greedy Queens (see A065188) below main diagonal.
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12
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4, 5, 10, 11, 13, 15, 20, 21, 26, 27, 29, 31, 34, 38, 40, 42, 43, 49, 50, 54, 56, 58, 59, 64, 67, 69, 71, 75, 77, 78, 80, 85, 86, 90, 91, 95, 99, 101, 102, 104, 108, 111, 113, 116, 117, 120, 123, 128, 129, 132, 133, 136, 141, 143, 144, 146, 151, 152, 154, 156, 160
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OFFSET
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1,1
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COMMENTS
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The word "below" in the definition is somewhat ambiguous. More precisely, this is the list of n such that A065188(n) < n. - N. J. A. Sloane, Aug 18 2016
For Greedy Queens that do not attack along antidiagonals, the analogous sequence of indices is A026352.
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LINKS
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EXAMPLE
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Greedy Queens take positions (1,1) (2,3) (3,5) (4,2) (5,4) (6,9) ... and the 4th and 5th are below the main diagonal, so a(1)=4 and a(2)=5.
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MATHEMATICA
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<<DiscreteMath`Combinatorica`;
base2=Table[{i, j}, {i, 0, 256}, {j, Floor[i/2], 2i}];
base3=DeleteCases[base2, {k_, l_}/; Or[l<-2+Floor[k/GoldenRatio], l>2+Floor[k*GoldenRatio], And[l>3+Floor[k/GoldenRatio], l<Floor[k*GoldenRatio]]], 2 ];
standardQueens=Backtrack[base3, (And[UnsameQ@@ First /@ #, UnsameQ@@ Last/@ #, UnsameQ@@ Subtract@@@ #, UnsameQ@@ Plus@@@ #])&, True&, One];
Position[Subtract@@@ standardQueens, _?Positive]//Flatten
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CROSSREFS
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A275884 is the complementary sequence.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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