A276325 Diagonal indices of Greedy Queens (see A065188).

0, -1, 2, -2, 1, -3, 4, -4, 3, 6, -5, -6, 5, -7, 8, 7, -8, -9, 10, -10, 9, 12, -11, -12, 11, 13, -13, -14, 15, -15, 16, -16, 17, 14, -17, -18, 19, 18, -19, -20, 21, 22, -21, -22, 23, 20, -23, -24, 24, -25, 25, 26, -26, 27, -27, -28, 29, -29, 30, -30, 28, 31

Offset

1,3

Comments

a(n) is the index of the diagonal of the n-th queen. The main diagonal has index 0, upper (lower) diagonals have positive (negative) indices.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

Equals A275901 - A275902.

Example

The first queen is in the main diagonal, the second queen is in the first lower diagonal, the third queen is in the second upper diagonal, ... :
:
:  Q\\\\ ...
:  \\\Q\ ...
:  \Q\\\ ...
:  \\\\Q ...
:  \\Q\\ ...
:  \\\\\ ...
:  .....

Maple

# Maple program from N. J. A. Sloane, Oct 03 2016
# To get 10000 terms of A275902 (xx), A275901 (yy), A276783 (ss), -A276325 (dd)
M1:=100000; M2:=22000; M3:=10000;
xx:=Array(0..M1, 0); yy:=Array(0..M1, 0); ss:=Array(0..M1, 0); dd:=Array(0..M1, 0);
xx[0]:=0; yy[0]:=0; ss[0]:=0; dd[0]:=0;
for n from 1 to M2 do
sw:=-1;
   for s from ss[n-1]+1 to M2 do
      for i from 0 to s do
         x:=s-i; y:=i;
         if not member(x, xx, 'p') and
            not member(y, yy, 'p') and
            not member(x-y, dd, 'p') then sw:=1; break; fi;
      od:  # od i
if sw=1 then break; fi;
   od: # od s
  if sw=-1 then lprint("error, n=", n); break; fi;
xx[n]:=x; yy[n]:=y; ss[n]:=x+y; dd[n]:=x-y;
od: # od n
[seq(xx[i], i=0..M3)]:
[seq(yy[i], i=0..M3)]:
[seq(ss[i], i=0..M3)]:
[seq(dd[i], i=0..M3)]:

Crossrefs

Cf. A065188, A276324, A275901, A275902.

Sequence in context: A286468 A102563 A121496 * A286548 A256134 A091971

Adjacent sequences: A276322 A276323 A276324 * A276326 A276327 A276328

Keyword

sign

Author

Alois P. Heinz, Aug 30 2016

Status

approved