%I #18 Aug 30 2021 17:12:26
%S 0,0,0,1,44,450,3175,17977,91326,433434,1968268,8674028,37428470,
%T 159059732
%N Number of 4-divided words of length n over a 4-letter alphabet.
%C See A210109 for further information.
%C Row sums of the following table which shows how many words of length n over a 4-letter alphabet are 4-divided in k>=1 different ways:
%C 1;
%C 38, 4, 2;
%C 253, 104, 66, 15, 3, 8, 0, 1;
%C 1333, 684, 475, 231, 130, 167, 55, 41, 25, 11, 9, 9, 1, 2, 2;
%C - _R. J. Mathar_, Mar 25 2012
%o (Python)
%o from itertools import product, combinations, permutations
%o def is4div(b):
%o for i, j, k in combinations(range(1, len(b)), 3):
%o divisions = [b[:i], b[i:j], b[j:k], b[k:]]
%o all_greater = True
%o for p, bp in enumerate(permutations(divisions)):
%o if p == 0: continue
%o if b >= "".join(bp): all_greater = False; break
%o if all_greater: return True
%o return False
%o def a(n): return sum(is4div("".join(b)) for b in product("0123", repeat=n))
%o print([a(n) for n in range(1, 9)]) # _Michael S. Branicky_, Aug 30 2021
%Y Cf. A210109, A210425.
%K nonn
%O 1,5
%A _R. J. Mathar_, Mar 21 2012
%E a(11)-a(14) from _Michael S. Branicky_, Aug 30 2021