This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A210324 #28 Aug 28 2021 12:45:04 %S A210324 0,0,1,16,78,324,1141,3885,12630,40315,126604,393986,1216525,3737912, %T A210324 11438230,34898189,106217986,322683051 %N A210324 Number of 3-divided words of length n over a 3-letter alphabet. %C A210324 See A210109 for further information. %C A210324 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 A210324 1; %C A210324 12, 3, 1; %C A210324 29, 29, 12, 5, 2, 1; %C A210324 100, 56, 69, 40, 21, 21, 11, 3, 2, 1; %C A210324 247, 183, 188, 115, 101, 96, 71, 40, 44, 27, 17, 6, 3, 2, 1; %C A210324 716, 474, 546, 328, 323, 268, 246, 203, 186, 140, 128, 100, 79, 56, 49, 22, 9, 6, 3, 2, 1; %C A210324 - _R. J. Mathar_, Mar 25 2012 %D A210324 Computed by _David Scambler_, Mar 19 2012 %o A210324 (Python) %o A210324 from itertools import product %o A210324 def is3div(b): %o A210324 for i in range(1, len(b)-1): %o A210324 for j in range(i+1, len(b)): %o A210324 X, Y, Z = b[:i], b[i:j], b[j:] %o A210324 if all(b < bp for bp in [X+Z+Y, Z+Y+X, Y+X+Z, Y+Z+X, Z+X+Y]): %o A210324 return True %o A210324 return False %o A210324 def a(n): return sum(is3div("".join(b)) for b in product("012", repeat=n)) %o A210324 print([a(n) for n in range(1, 11)]) # _Michael S. Branicky_, Aug 28 2021 %Y A210324 Cf. A210109, A210325, A210326. %K A210324 nonn,more %O A210324 1,4 %A A210324 _N. J. A. Sloane_, Mar 20 2012 %E A210324 After a typo was corrected, the entries were confirmed by _R. J. Mathar_, Mar 22 2012 %E A210324 a(14)-a(18) from _Michael S. Branicky_, Aug 28 2021