A007687 Number of 4-colorings of cyclic group of order n. (Formerly M2833)

3, 10, 21, 44, 83, 218, 271, 692, 865, 2622, 2813, 9220, 9735, 35214, 35911, 135564, 136899

Offset

1,1

Comments

The number of 2-colorings of Z_n is A000034(n-1), the number of 3-colorings of Z_n is A005843(n). It seems that the number of n-colorings of Z_2 is A137928(n-1). - Andrey Zabolotskiy, Oct 02 2017

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..17.

R. Haas, Three-colorings of finite groups or an algebra of nonequalities, Math. Mag., 63 (1990), 211-225.

R. Haas, Letter to N. J. A. Sloane, Aug. 1994

Prog

(Python)
def colorings(n, zp):
    result = 0
    f = [0]*zp
    for i in range(n**zp):
        for j1 in range(zp):
            for j2 in range(zp):
                if (f[j1]+f[j2])%n == f[(j1+j2)%zp]:
                    break
            else:
                continue
            break
        else:
            result += 1
        f[0] += 1
        for j in range(zp-1):
            if f[j] == n:
                f[j] = 0
                f[j+1] += 1
    return result
print([colorings(4, k) for k in range(1, 12)])
# Andrey Zabolotskiy, Jul 12 2017

Crossrefs

Cf. A007688.

Sequence in context: A207380 A268348 A117495 * A330273 A335666 A192033

Adjacent sequences: A007684 A007685 A007686 * A007688 A007689 A007690

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(6)-a(11) from Andrey Zabolotskiy, Jul 12 2017

a(12)-a(17) from Andrey Zabolotskiy, Oct 02 2017

Status

approved