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A007687 Number of 4-colorings of cyclic group of order n.

%I A007687 M2833 #32 Sep 26 2024 23:37:25
%S A007687 3,10,21,44,83,218,271,692,865,2622,2813,9220,9735,35214,35911,135564,
%T A007687 136899,533290,535081
%N A007687 Number of 4-colorings of cyclic group of order n.
%C A007687 The number of 2-colorings of Z_n is A000034(n-1), the number of 3-colorings of Z_n is A005843(n). The number of n-colorings of Z_2 is A137928(n-1). - _Andrey Zabolotskiy_, Oct 02 2017
%D A007687 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007687 Robert Haas, <a href="https://doi.org/10.2307/2690938">Three-colorings of finite groups or an algebra of nonequalities</a>, Math. Mag., 63 (1990), 211-225.
%H A007687 Robert Haas, <a href="/A007687/a007687.pdf">Letter to N. J. A. Sloane, Aug. 1994</a>
%o A007687 (Python)
%o A007687 from itertools import product
%o A007687 def colorings(n, zp):
%o A007687     result = 0
%o A007687     for f in product(range(n), repeat=zp):
%o A007687         for j1 in range(zp):
%o A007687             for j2 in range(zp):
%o A007687                 if (f[j1]+f[j2])%n == f[(j1+j2)%zp]:
%o A007687                     break
%o A007687             else:
%o A007687                 continue
%o A007687             break
%o A007687         else:
%o A007687             result += 1
%o A007687     return result
%o A007687 print([colorings(4, k) for k in range(1, 12)])
%o A007687 # _Andrey Zabolotskiy_, Jul 12 2017
%Y A007687 Cf. A007688.
%K A007687 nonn,more,hard
%O A007687 1,1
%A A007687 _N. J. A. Sloane_
%E A007687 a(6)-a(11) from _Andrey Zabolotskiy_, Jul 12 2017
%E A007687 a(12)-a(17) from _Andrey Zabolotskiy_, Oct 02 2017
%E A007687 a(18)-a(19) from _Lucas A. Brown_, Sep 20 2024