cp's OEIS Frontend

A219744 The number of 2 X 2 symmetric positive definite matrices whose entries are integers x,y,z satisfying x^2 + y^2 + z^2 <= n^2.

%I A219744 #8 Jan 14 2017 01:34:23
%S A219744 0,1,10,22,49,92,150,227,328,449,609,792,1017,1281,1582,1911,2308,
%T A219744 2750,3241,3778,4420,5049,5776,6572,7429,8378,9413,10505,11646,12935,
%U A219744 14251,15690,17235,18854,20580,22391,24330,26352,28541,30750
%N A219744 The number of 2 X 2 symmetric positive definite matrices whose entries are integers x,y,z satisfying x^2 + y^2 + z^2 <= n^2.
%p A219744 a:=proc(n)
%p A219744 local x,y,z,count,num;
%p A219744 count:=0;
%p A219744 for x from 0 to n do
%p A219744 for y from 0 to n do
%p A219744 for z from -n to n do
%p A219744 if x^2+y^2+z^2 > n^2 then next; fi;
%p A219744 if x>0 and x*y > z^2 then count:=count+1; fi;
%p A219744 od:
%p A219744 od:
%p A219744 od:
%p A219744 count;
%p A219744 end:
%Y A219744 Cf. A219693.
%K A219744 nonn
%O A219744 1,3
%A A219744 _W. Edwin Clark_, Nov 26 2012