A380832 - OEIS

%I #17 Feb 12 2025 14:22:37

%S 1,1,49,169,625,1465,3337,5689,10009,15937,24865,35761,51265,69817,

%T 94849,124009,161497,204529,260137,320497,394705,478705,577489,687913,

%U 819313,960457,1127785,1309153,1517161,1742497,2001505,2273473,2585905,2920009,3297337,3700153,4144105,4618657,5145865,5703073

%N Number of points in Z^4 of norm <= n where the sum of the four entries is even.

%C Points in Z^4 with even sum of entries forms the D_4 lattice. That is to say, the sequence is the "ball" pattern on D_4 lattice.

%C a(n) == 1 (mod 24).

%H Steven Lu, <a href="/A380832/a380832.py.txt">Python program</a>

%e a(2) = 49, because in the ball with radius 2, there is 1 point (0,0,0,0), 8 points similar to (0,0,0,2), 24 points similar to (0,0,1,1), and 16 points similar to (1,1,1,1).

%o (Python) # See _Steven Lu_'s link

%o (PARI) a(n) = sum(x=-n, n, sum(y=-n, n, sum(z=-n, n, sum(t=-n, n, (((x+y+z+t) % 2)==0) && (x^2+y^2+z^2+t^2 <=n^2))))); \\ _Michel Marcus_, Feb 09 2025

%Y Cf. A055410.

%K nonn,new

%O 0,3

%A _Steven Lu_, Feb 05 2025