A210426 Number of 4-divided words of length n over a 4-letter alphabet.

0, 0, 0, 1, 44, 450, 3175, 17977, 91326, 433434, 1968268, 8674028, 37428470, 159059732

Offset: 1

Author

R. J. Mathar, Mar 21 2012

Keywords

• nonn

Comments

See A210109 for further information.

Row sums of the following table which shows how many words of length n over a 4-letter alphabet are 4-divided in k>=1 different ways:

1;

38, 4, 2;

253, 104, 66, 15, 3, 8, 0, 1;

1333, 684, 475, 231, 130, 167, 55, 41, 25, 11, 9, 9, 1, 2, 2;

- R. J. Mathar, Mar 25 2012

Crossrefs

Cf. A210109, A210425.

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("0123", repeat=n))
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Aug 30 2021

Extensions

a(11)-a(14) from Michael S. Branicky, Aug 30 2021