A210322 Number of 5-divided binary words of length n.

0, 0, 0, 0, 0, 0, 0, 0, 6, 36, 150, 464, 1304, 3349, 8213, 19230, 43867, 97644, 213776, 461240, 984603, 2082436

Offset: 1

Author

N. J. A. Sloane, Mar 20 2012

Keywords

• nonn
• more

Comments

See A210109 for further information.

References

• Computed by David Scambler, Mar 19 2012

Crossrefs

Cf. A210109, A210321.

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("01", repeat=n))
print([a(n) for n in range(1, 13)]) # Michael S. Branicky, Aug 27 2021

Extensions

a(17)-a(22) from Michael S. Branicky, Aug 27 2021