%I #16 Jun 07 2017 00:35:17

%S 0,0,2,7,12,20,0,63,116,72,90,131,0,108,182,339,240,602,324,415,326,

%T 420,462,839,604,216,1808,763,756,812,810,1735,992,1056,1092,3311,648,

%U 1620,650,2511,1560,1640,1134,2227,4328,1980,2070,3683,2484,2644,2450,1519

%N a(n) is the number of ordered solutions (x,y,z) to x^3 + y^3 == z^3 mod n with 1 <= x,y,z <= n-1.

%C Record values of A137401: 0, 2, 7, 12, 20, 63, 116, 131, 182, 339, 602, 839, 1808, 3311, 4328, 7964, 8864, 9231, 19583, 21986, 41363, 52676, 81467, 87596, 92087, 112616, 236951, 247940, 378071, 386423, 521135, ... - _Robert G. Wilson v_

%H Chai Wah Wu, <a href="/A137401/b137401.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..425 from Robert G. Wilson v)

%F a(n) = A063454(n)-3*A087786(n)+3*A000189(n)-1. - _Vladeta Jovovic_, Apr 11 2008

%e a(4)=7 because (1, 2, 1), (1, 3, 2), (2, 1, 1), (2, 2, 2), (2, 3, 3), (3, 1, 2), (3, 2, 3) are solutions for n=4.

%t f[n_] := Block[ {c = 0}, Do[ If[ Mod[x^3 + y^3, n] == Mod[z^3, n], c++ ], {x, n - 1}, {y, n - 1}, {z, n - 1}]; c];

%t Table[Length[Select[Tuples[Range[n - 1], 3], Mod[ #[[1]]^3 + #[[2]]^3 - #[[3]]^3, n] == 0 &]], {n, 2, 50}] (* _Stefan Steinerberger_, Apr 12 2008 *)

%o (Python)

%o def A137401(n):

%o ndict = {}

%o for i in range(1,n):

%o m = pow(i,3,n)

%o if m in ndict:

%o ndict[m] += 1

%o else:

%o ndict[m] = 1

%o count = 0

%o for i in ndict:

%o ni = ndict[i]

%o for j in ndict:

%o k = (i+j) % n

%o if k in ndict:

%o count += ni*ndict[j]*ndict[k]

%o return count # _Chai Wah Wu_, Jun 06 2017

%Y Cf. A063454.

%K nonn

%O 1,3

%A Neven Juric (neven.juric(AT)apis-it.hr), Apr 11 2008

%E More terms from _Stefan Steinerberger_ and _Robert G. Wilson v_, Apr 12 2008