A210326 Number of 5-divided words of length n over a 3-letter alphabet.

0, 0, 0, 0, 0, 0, 15, 166, 1135, 5865, 26170, 105224, 396082, 1419981, 4916112

Offset

1,7

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 5-divided in k>=1 different ways:

15;

103,43,20;

546,236,162,84,28,51,16,8,5;

2118,1211,848,480,...

- R. J. Mathar, Mar 25 2012

References

Computed by David Scambler, Mar 19 2012

Links

Table of n, a(n) for n=1..15.

Prog

(Python)
from itertools import product, combinations, permutations
def is5div(b):
    for i, j, k, l in combinations(range(1, len(b)), 4):
        divisions = [b[:i], b[i:j], b[j:k], b[k:l], b[l:]]
        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(is5div("".join(b)) for b in product("012", repeat=n))
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Aug 28 2021

Crossrefs

Cf. A210109, A210324, A210325.

Sequence in context: A229406 A118093 A167615 * A016234 A160197 A055660

Adjacent sequences: A210323 A210324 A210325 * A210327 A210328 A210329

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 20 2012

Extensions

a(14)-a(15) from Michael S. Branicky, Aug 28 2021

Status

approved