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). 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
Robert Haas, Three-colorings of finite groups or an algebra of nonequalities, Math. Mag., 63 (1990), 211-225.
Robert Haas, Letter to N. J. A. Sloane, Aug. 1994
PROG
(Python)
from itertools import product
def colorings(n, zp):
result = 0
for f in product(range(n), repeat=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
return result
print([colorings(4, k) for k in range(1, 12)])
# Andrey Zabolotskiy, Jul 12 2017
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
EXTENSIONS
a(6)-a(11) from Andrey Zabolotskiy, Jul 12 2017
a(12)-a(17) from Andrey Zabolotskiy, Oct 02 2017
a(18)-a(19) from Lucas A. Brown, Sep 20 2024
STATUS
approved