A210324 Number of 3-divided words of length n over a 3-letter alphabet.

0, 0, 1, 16, 78, 324, 1141, 3885, 12630, 40315, 126604, 393986, 1216525, 3737912, 11438230, 34898189, 106217986, 322683051

Offset

1,4

Comments

See A210109 for further information.

Row sums of the following irregular triangle which shows how many words of length n over a 3-letter alphabet are 3-divided in k>=1 different ways:

1;

12, 3, 1;

29, 29, 12, 5, 2, 1;

100, 56, 69, 40, 21, 21, 11, 3, 2, 1;

247, 183, 188, 115, 101, 96, 71, 40, 44, 27, 17, 6, 3, 2, 1;

716, 474, 546, 328, 323, 268, 246, 203, 186, 140, 128, 100, 79, 56, 49, 22, 9, 6, 3, 2, 1;

- R. J. Mathar, Mar 25 2012

References

Computed by David Scambler, Mar 19 2012

Links

Table of n, a(n) for n=1..18.

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("012", repeat=n))
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Aug 28 2021

Crossrefs

Cf. A210109, A210325, A210326.

Sequence in context: A303179 A061995 A212563 * A250231 A212896 A250279

Adjacent sequences: A210321 A210322 A210323 * A210325 A210326 A210327

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 20 2012

Extensions

After a typo was corrected, the entries were confirmed by R. J. Mathar, Mar 22 2012

a(14)-a(18) from Michael S. Branicky, Aug 28 2021

Status

approved