A210321 Number of 4-divided binary words of length n.

0, 0, 0, 0, 0, 1, 11, 37, 109, 287, 698, 1617, 3642, 7985, 17208, 36620, 77093, 161027, 334205, 690080, 1418917, 2907655, 5941148, 12110674

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, A210322.

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("01", repeat=n))
print([a(n) for n in range(1, 14)]) # Michael S. Branicky, Aug 27 2021

Extensions

a(18)-a(24) from Michael S. Branicky, Aug 27 2021