login
A199134
Indices of Greedy Queens (see A065188) below main diagonal.
12
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
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
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.
MATHEMATICA
<<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
CROSSREFS
Cf. A065188, A026352, A275893 (another version).
A275884 is the complementary sequence.
For runs see A275885, A275886.
Sequence in context: A092027 A084750 A323488 * A369654 A131855 A102858
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Nov 04 2011
STATUS
approved