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 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 &]]; 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

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