cp's OEIS Frontend

A210426 Number of 4-divided words of length n over a 4-letter alphabet.

%I A210426 #18 Aug 30 2021 17:12:26
%S A210426 0,0,0,1,44,450,3175,17977,91326,433434,1968268,8674028,37428470,
%T A210426 159059732
%N A210426 Number of 4-divided words of length n over a 4-letter alphabet.
%C A210426 See A210109 for further information.
%C A210426 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 A210426 1;
%C A210426 38, 4, 2;
%C A210426 253, 104, 66, 15, 3, 8, 0, 1;
%C A210426 1333, 684, 475, 231, 130, 167, 55, 41, 25, 11, 9, 9, 1, 2, 2;
%C A210426 - _R. J. Mathar_, Mar 25 2012
%o A210426 (Python)
%o A210426 from itertools import product, combinations, permutations
%o A210426 def is4div(b):
%o A210426     for i, j, k in combinations(range(1, len(b)), 3):
%o A210426         divisions = [b[:i], b[i:j], b[j:k], b[k:]]
%o A210426         all_greater = True
%o A210426         for p, bp in enumerate(permutations(divisions)):
%o A210426             if p == 0: continue
%o A210426             if b >= "".join(bp): all_greater = False; break
%o A210426         if all_greater: return True
%o A210426     return False
%o A210426 def a(n): return sum(is4div("".join(b)) for b in product("0123", repeat=n))
%o A210426 print([a(n) for n in range(1, 9)]) # _Michael S. Branicky_, Aug 30 2021
%Y A210426 Cf. A210109, A210425.
%K A210426 nonn
%O A210426 1,5
%A A210426 _R. J. Mathar_, Mar 21 2012
%E A210426 a(11)-a(14) from _Michael S. Branicky_, Aug 30 2021