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.

0, 1, 10, 22, 49, 92, 150, 227, 328, 449, 609, 792, 1017, 1281, 1582, 1911, 2308, 2750, 3241, 3778, 4420, 5049, 5776, 6572, 7429, 8378, 9413, 10505, 11646, 12935, 14251, 15690, 17235, 18854, 20580, 22391, 24330, 26352, 28541, 30750

Offset

1,3

Links

Table of n, a(n) for n=1..40.

Maple

a:=proc(n)
local x, y, z, count, num;
count:=0;
for x from 0 to n do
for y from 0 to n do
for z from -n to n do
if x^2+y^2+z^2 > n^2 then next; fi;
if x>0 and x*y > z^2 then count:=count+1; fi;
od:
od:
od:
count;
end:

Crossrefs

Cf. A219693.

Sequence in context: A216048 A079861 A014008 * A246419 A039315 A225708

Adjacent sequences: A219741 A219742 A219743 * A219745 A219746 A219747

Keyword

nonn

Author

W. Edwin Clark, Nov 26 2012

Status

approved