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%I #20 Aug 06 2018 13:21:52
%S 1,4,9,20,25,36,55,112,189,100,121,180,109,220,225,448,289,756,487,
%T 500,495,484,529,1008,725,436,2187,1100,841,900,1081,2048,1089,1156,
%U 1375,3780,973,1948,981,2800,1681,1980,1513,2420,4725,2116,2209,4032
%N Number of solutions to x^3 + y^3 = z^3 mod n.
%C Equivalently, the number of solutions to x^3 + y^3 + z^3 == 0 (mod n). - _Andrew Howroyd_, Jul 18 2018
%H Chai Wah Wu, <a href="/A063454/b063454.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..1000 from Seiichi Manyama)
%o (PARI) a(n)={my(p=Mod(sum(i=0, n-1, x^(i^3%n)), 1-x^n)); polcoeff(lift(p^3), 0)} \\ _Andrew Howroyd_, Jul 18 2018
%o (Python)
%o def A063454(n):
%o ndict = {}
%o for i in range(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 Number of solutions to x^k + y^k = z^k mod n: A062775 (k=2), this sequence (k=3), A288099 (k=4), A288100 (k=5), A288101 (k=6), A288102 (k=7), A288103 (k=8), A288104 (k=9), A288105 (k=10).
%K nonn,mult
%O 1,2
%A Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 25 2001
%E More terms from _Dean Hickerson_, Jul 26, 2001
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