A210325 Number of 4-divided words of length n over a 3-letter alphabet.

0, 0, 0, 0, 6, 56, 343, 1534, 6067, 22162, 76899, 257792, 843616, 2712241, 8606426, 27040628, 84311895

Offset: 1

Author

N. J. A. Sloane, Mar 20 2012

Keywords

• nonn
• more

Comments

See A210109 for further information.

Row sums of the following table which shows how many words of length n over a 3-letter alphabet are 4-divided in k different ways:

6;

34, 13, 9;

159, 75, 51, 20, 13, 17, 5, 3;

500, 287, 266, 130, 71, 103, 37, 35, 33, 22, 15, 14, 13, 2, 3, 1, 2;

- R. J. Mathar, Mar 25 2012

References

• Computed by David Scambler, Mar 19 2012

Crossrefs

Cf. A210109, A210324, A210326.

Programs

Python

from itertools import product, combinations, permutations
def is4div(b):
    for i, j, k in combinations(range(1, len(b)), 3):
        divisions = [b[:i], b[i:j], b[j:k], b[k:]]
        all_greater = True
        for p, bp in enumerate(permutations(divisions)):
            if p == 0: continue
            if b >= "".join(bp): all_greater = False; break
        if all_greater: return True
    return False
def a(n): return sum(is4div("".join(b)) for b in product("012", repeat=n))
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Aug 28 2021

Extensions

a(14)-a(17) from Michael S. Branicky, Aug 28 2021