A210324 - OEIS

%I #28 Aug 28 2021 12:45:04

%S 0,0,1,16,78,324,1141,3885,12630,40315,126604,393986,1216525,3737912,

%T 11438230,34898189,106217986,322683051

%N Number of 3-divided words of length n over a 3-letter alphabet.

%C See A210109 for further information.

%C Row sums of the following irregular triangle which shows how many words of length n over a 3-letter alphabet are 3-divided in k>=1 different ways:

%C 1;

%C 12, 3, 1;

%C 29, 29, 12, 5, 2, 1;

%C 100, 56, 69, 40, 21, 21, 11, 3, 2, 1;

%C 247, 183, 188, 115, 101, 96, 71, 40, 44, 27, 17, 6, 3, 2, 1;

%C 716, 474, 546, 328, 323, 268, 246, 203, 186, 140, 128, 100, 79, 56, 49, 22, 9, 6, 3, 2, 1;

%C - _R. J. Mathar_, Mar 25 2012

%D Computed by _David Scambler_, Mar 19 2012

%o (Python)

%o from itertools import product

%o def is3div(b):

%o     for i in range(1, len(b)-1):

%o         for j in range(i+1, len(b)):

%o             X, Y, Z = b[:i], b[i:j], b[j:]

%o             if all(b < bp for bp in [X+Z+Y, Z+Y+X, Y+X+Z, Y+Z+X, Z+X+Y]):

%o                 return True

%o     return False

%o def a(n): return sum(is3div("".join(b)) for b in product("012", repeat=n))

%o print([a(n) for n in range(1, 11)]) # _Michael S. Branicky_, Aug 28 2021

%Y Cf. A210109, A210325, A210326.

%K nonn,more

%O 1,4

%A _N. J. A. Sloane_, Mar 20 2012

%E After a typo was corrected, the entries were confirmed by _R. J. Mathar_, Mar 22 2012

%E a(14)-a(18) from _Michael S. Branicky_, Aug 28 2021