A276325 - OEIS

%I #12 Oct 03 2016 17:50:11

%S 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,

%T 13,-13,-14,15,-15,16,-16,17,14,-17,-18,19,18,-19,-20,21,22,-21,-22,

%U 23,20,-23,-24,24,-25,25,26,-26,27,-27,-28,29,-29,30,-30,28,31

%N Diagonal indices of Greedy Queens (see A065188).

%C 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.

%H Alois P. Heinz, <a href="/A276325/b276325.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals A275901 - A275902.

%e 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, ... :

%e :

%e :  Q\\\\ ...

%e :  \\\Q\ ...

%e :  \Q\\\ ...

%e :  \\\\Q ...

%e :  \\Q\\ ...

%e :  \\\\\ ...

%e :  .....

%p # Maple program from _N. J. A. Sloane_, Oct 03 2016

%p # To get 10000 terms of A275902 (xx), A275901 (yy), A276783 (ss), -A276325 (dd)

%p M1:=100000; M2:=22000; M3:=10000;

%p xx:=Array(0..M1,0); yy:=Array(0..M1,0); ss:=Array(0..M1,0); dd:=Array(0..M1,0);

%p xx[0]:=0; yy[0]:=0; ss[0]:=0; dd[0]:=0;

%p for n from 1 to M2 do

%p sw:=-1;

%p    for s from ss[n-1]+1 to M2 do

%p       for i from 0 to s do

%p          x:=s-i; y:=i;

%p          if not member(x,xx,'p') and

%p             not member(y,yy,'p') and

%p             not member(x-y,dd,'p') then sw:=1; break; fi;

%p       od:  # od i

%p if sw=1 then break; fi;

%p    od: # od s

%p   if sw=-1 then lprint("error, n=",n); break; fi;

%p xx[n]:=x; yy[n]:=y; ss[n]:=x+y; dd[n]:=x-y;

%p od: # od n

%p [seq(xx[i],i=0..M3)]:

%p [seq(yy[i],i=0..M3)]:

%p [seq(ss[i],i=0..M3)]:

%p [seq(dd[i],i=0..M3)]:

%Y Cf. A065188, A276324, A275901, A275902.

%K sign

%O 1,3

%A _Alois P. Heinz_, Aug 30 2016