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A276325 Diagonal indices of Greedy Queens (see A065188).

%I A276325 #12 Oct 03 2016 17:50:11
%S A276325 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 A276325 13,-13,-14,15,-15,16,-16,17,14,-17,-18,19,18,-19,-20,21,22,-21,-22,
%U A276325 23,20,-23,-24,24,-25,25,26,-26,27,-27,-28,29,-29,30,-30,28,31
%N A276325 Diagonal indices of Greedy Queens (see A065188).
%C A276325 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 A276325 Alois P. Heinz, <a href="/A276325/b276325.txt">Table of n, a(n) for n = 1..10000</a>
%F A276325 Equals A275901 - A275902.
%e A276325 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 A276325 :
%e A276325 :  Q\\\\ ...
%e A276325 :  \\\Q\ ...
%e A276325 :  \Q\\\ ...
%e A276325 :  \\\\Q ...
%e A276325 :  \\Q\\ ...
%e A276325 :  \\\\\ ...
%e A276325 :  .....
%p A276325 # Maple program from _N. J. A. Sloane_, Oct 03 2016
%p A276325 # To get 10000 terms of A275902 (xx), A275901 (yy), A276783 (ss), -A276325 (dd)
%p A276325 M1:=100000; M2:=22000; M3:=10000;
%p A276325 xx:=Array(0..M1,0); yy:=Array(0..M1,0); ss:=Array(0..M1,0); dd:=Array(0..M1,0);
%p A276325 xx[0]:=0; yy[0]:=0; ss[0]:=0; dd[0]:=0;
%p A276325 for n from 1 to M2 do
%p A276325 sw:=-1;
%p A276325    for s from ss[n-1]+1 to M2 do
%p A276325       for i from 0 to s do
%p A276325          x:=s-i; y:=i;
%p A276325          if not member(x,xx,'p') and
%p A276325             not member(y,yy,'p') and
%p A276325             not member(x-y,dd,'p') then sw:=1; break; fi;
%p A276325       od:  # od i
%p A276325 if sw=1 then break; fi;
%p A276325    od: # od s
%p A276325   if sw=-1 then lprint("error, n=",n); break; fi;
%p A276325 xx[n]:=x; yy[n]:=y; ss[n]:=x+y; dd[n]:=x-y;
%p A276325 od: # od n
%p A276325 [seq(xx[i],i=0..M3)]:
%p A276325 [seq(yy[i],i=0..M3)]:
%p A276325 [seq(ss[i],i=0..M3)]:
%p A276325 [seq(dd[i],i=0..M3)]:
%Y A276325 Cf. A065188, A276324, A275901, A275902.
%K A276325 sign
%O A276325 1,3
%A A276325 _Alois P. Heinz_, Aug 30 2016