A210426 - OEIS

%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