login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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 (list; graph; refs; listen; history; text; internal format)
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: A152023 A165798 A158693 * A300162 A211259 A069758

Adjacent sequences:  A319614 A319615 A319616 * A319618 A319619 A319620

KEYWORD

nonn,easy

AUTHOR

Brian J. Harrild, Sep 24 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 12:22 EDT 2021. Contains 343150 sequences. (Running on oeis4.)