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

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 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

Crossrefs

Cf. A210109, A210324, A210325.

Programs

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

Extensions

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