login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A295848 Number of nonnegative solutions to (x,y,z) = 1 and x^2 + y^2 + z^2 = n. 3
0, 3, 3, 1, 0, 6, 3, 0, 0, 3, 6, 3, 0, 6, 6, 0, 0, 9, 3, 3, 0, 6, 3, 0, 0, 6, 12, 3, 0, 12, 6, 0, 0, 6, 9, 6, 0, 6, 9, 0, 0, 15, 6, 3, 0, 6, 6, 0, 0, 6, 12, 6, 0, 12, 9, 0, 0, 6, 6, 9, 0, 12, 12, 0, 0, 18, 12, 3, 0, 12, 6, 0, 0, 9, 18, 6, 0, 12, 6, 0, 0, 9, 9, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)=0 for n in A047536. - Robert Israel, Nov 30 2017

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000 (n=0..200 from Seiichi Manyama)

EXAMPLE

a(1) = 3;

(1,0,0) = 1 and 1^2 + 0^2 + 0^2 = 1.

(0,1,0) = 1 and 0^2 + 1^2 + 0^2 = 1.

(0,0,1) = 1 and 0^2 + 0^2 + 1^2 = 1.

a(2) = 3;

(1,1,0) = 1 and 1^2 + 1^2 + 0^2 = 2.

(1,0,1) = 1 and 1^2 + 0^2 + 1^2 = 2.

(0,1,1) = 1 and 0^2 + 1^2 + 1^2 = 2.

a(3) = 1;

(1,1,1) = 1 and 1^2 + 1^2 + 1^2 = 3.

a(5) = 6;

(2,1,0) = 1 and 2^2 + 1^2 + 0^2 = 5.

(2,0,1) = 1 and 2^2 + 0^2 + 1^2 = 5.

(1,2,0) = 1 and 1^2 + 2^2 + 0^2 = 5.

(1,0,2) = 1 and 1^2 + 0^2 + 2^2 = 5.

(0,2,1) = 1 and 0^2 + 2^2 + 1^2 = 5.

(0,1,2) = 1 and 0^2 + 1^2 + 2^2 = 5.

MAPLE

N:= 100:

V:= Array(0..N):

for x from 0 to floor(sqrt(N/3)) do

  for y from x to floor(sqrt((N-x^2)/2)) do

    for z from y to floor(sqrt(N-x^2-y^2)) do

      if igcd(x, y, z) = 1 then

        r:= x^2 + y^2 + z^2;

        m:= nops({x, y, z});

        if m=3 then V[r]:= V[r]+6

        elif m=2 then V[r]:= V[r]+3

        else V[r]:= V[r]+1

        fi

      fi

od od od:

convert(V, list); # Robert Israel, Nov 30 2017

MATHEMATICA

f[n_] := Total[ Length@ Permutations@# & /@ Select[ PowersRepresentations[n, 3, 2], GCD[#[[1]], #[[2]], #[[3]]] == 1 &]]; Array[f, 90, 0] (* Robert G. Wilson v, Nov 30 2017 *)

CROSSREFS

Cf. A002102, A047536, A048240, A295819, A295849.

Sequence in context: A245669 A211648 A261634 * A226785 A245974 A316989

Adjacent sequences:  A295845 A295846 A295847 * A295849 A295850 A295851

KEYWORD

nonn,easy,look

AUTHOR

Seiichi Manyama, Nov 29 2017

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 04:41 EDT 2022. Contains 353851 sequences. (Running on oeis4.)