login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007687 Number of 4-colorings of cyclic group of order n.
(Formerly M2833)
2
3, 10, 21, 44, 83, 218, 271, 692, 865, 2622, 2813, 9220, 9735, 35214, 35911, 135564, 136899 (list; graph; refs; listen; history; text; internal format)
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. Hass, 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 * A192033 A295063 A298856

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 09:05 EDT 2019. Contains 327128 sequences. (Running on oeis4.)