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A210425 Number of 3-divided words of length n over a 4-letter alphabet.

%I A210425 #15 Aug 30 2021 10:54:56
%S A210425 0,0,4,60,374,1960,9103,40497,174127,735268,3064477,12664101,52005445,
%T A210425 212595280,866047122
%N A210425 Number of 3-divided words of length n over a 4-letter alphabet.
%C A210425 See A210109 for further information.
%C A210425 Row sums of the following table which shows how many words of length n over a 4-letter alphabet are 3-divided in k>=1 different ways:
%C A210425 4;
%C A210425 41, 14, 5;
%C A210425 147, 111, 67, 29, 14, 6;
%C A210425 594, 358, 381, 211, 156, 128, 80, 28, 17, 7;
%C A210425 2072, 1400, 1433, 875, 821, 669, 588, 369, 340, 240, 163, 72, 33, 20, 8;
%C A210425 - _R. J. Mathar_, Mar 25 2012
%o A210425 (Python)
%o A210425 from itertools import product
%o A210425 def is3div(b):
%o A210425     for i in range(1, len(b)-1):
%o A210425         for j in range(i+1, len(b)):
%o A210425             X, Y, Z = b[:i], b[i:j], b[j:]
%o A210425             if all(b < bp for bp in [X+Z+Y, Z+Y+X, Y+X+Z, Y+Z+X, Z+X+Y]):
%o A210425                 return True
%o A210425     return False
%o A210425 def a(n): return sum(is3div("".join(b)) for b in product("0123", repeat=n))
%o A210425 print([a(n) for n in range(1, 9)]) # _Michael S. Branicky_, Aug 30 2021
%Y A210425 Cf. A210109, A210426.
%K A210425 nonn
%O A210425 1,3
%A A210425 _R. J. Mathar_, Mar 21 2012
%E A210425 a(12)-a(15) from _Michael S. Branicky_, Aug 30 2021