A199134 - OEIS

A199134

Indices of Greedy Queens (see A065188) below main diagonal.

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

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

N. J. A. Sloane, Table of n, a(n) for n = 1..19098

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

Adjacent sequences: A199131 A199132 A199133 * A199135 A199136 A199137

KEYWORD

nonn

AUTHOR

Wouter Meeussen, Nov 04 2011

STATUS

approved