A319617 Number of Integer solutions to w^2 + x^2 + y^2 + z^2 < n^2; number of lattice points inside a 4-sphere of radius n.

0, 1, 65, 321, 1257, 2873, 6265, 11377, 20161, 31665, 48945, 71401, 102041, 139481, 188753, 247329, 323697, 409457, 516121, 640393, 789161, 955793, 1153025, 1376305, 1637929, 1921049, 2252889, 2615673, 3033665, 3483633, 3990753, 4547945, 5173145, 5840393, 6589945, 7395921, 8287297, 9238001, 10281977, 11402457, 12633145, 13929377

Offset

0,3

Links

Table of n, a(n) for n=0..41.

Example

For n=2 there are 65 lattice points in Z^4 such that w^2+x^2+y^2+x^2 < 4

Prog

(Python)
for n in range (0, 51):
    NumPoints=0
    for w in range (-n, n+1):
        for x in range (-n, n+1):
            for y in range (-n, n+1):
                for z in range (-n, n+1):
                    if w**2+x**2+y**2+z**2<n**2:
                        NumPoints+=1
    print (n, NumPoints)

Crossrefs

a(n) = A055410(n) - A267326(n).

Sequence in context: A165798 A158693 A365874 * A300162 A211259 A069758

Adjacent sequences: A319614 A319615 A319616 * A319618 A319619 A319620

Keyword

nonn,easy

Author

Brian J. Harrild, Sep 24 2018

Status

approved