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

1,5

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

Links

Table of n, a(n) for n=1..14.

Prog

(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

Crossrefs

Cf. A210109, A210425.

Sequence in context: A250337 A002613 A094201 * A231242 A221730 A306036

Adjacent sequences: A210423 A210424 A210425 * A210427 A210428 A210429

Keyword

nonn

Author

R. J. Mathar, Mar 21 2012

Extensions

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

Status

approved