

A210425


Number of 3divided words of length n over a 4letter alphabet.


2



0, 0, 4, 60, 374, 1960, 9103, 40497, 174127, 735268, 3064477, 12664101, 52005445, 212595280, 866047122
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OFFSET

1,3


COMMENTS

See A210109 for further information.
Row sums of the following table which shows how many words of length n over a 4letter alphabet are 3divided in k>=1 different ways:
4;
41, 14, 5;
147, 111, 67, 29, 14, 6;
594, 358, 381, 211, 156, 128, 80, 28, 17, 7;
2072, 1400, 1433, 875, 821, 669, 588, 369, 340, 240, 163, 72, 33, 20, 8;


LINKS



PROG

(Python)
from itertools import product
def is3div(b):
for i in range(1, len(b)1):
for j in range(i+1, len(b)):
X, Y, Z = b[:i], b[i:j], b[j:]
if all(b < bp for bp in [X+Z+Y, Z+Y+X, Y+X+Z, Y+Z+X, Z+X+Y]):
return True
return False
def a(n): return sum(is3div("".join(b)) for b in product("0123", repeat=n))


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



