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

1,7

Comments

See A210109 for further information.

References

Computed by David Scambler, Mar 19 2012

Links

Table of n, a(n) for n=1..24.

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

Crossrefs

Cf. A210109, A210322.

Sequence in context: A075024 A229612 A297797 * A356278 A355630 A306423

Adjacent sequences: A210318 A210319 A210320 * A210322 A210323 A210324

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 20 2012

Extensions

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

Status

approved