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 A257063 #8 Dec 20 2018 16:10:14 %S A257063 1,2,3,3,4,4,5,6,7,7,8,8,9,10,11,11,12,12,13,14,15,15,16,16,17,18,19, %T A257063 19,20,20,21,22,23,23,24,24,25,26,27,27,28,28,29,30,31,31,32,32,33,34, %U A257063 35,35,36,36,37,38,39,39,40,40,41,42,43,43,44,44,45,46,47,47,48,48,49,50,51,51 %N A257063 Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2 or 3. %H A257063 R. H. Hardin, <a href="/A257063/b257063.txt">Table of n, a(n) for n = 1..210</a> %F A257063 Empirical: a(n) = a(n-1) + a(n-6) - a(n-7). %F A257063 Empirical for n mod 6 = 0: a(n) = (2/3)*n %F A257063 Empirical for n mod 6 = 1: a(n) = (2/3)*n + (1/3) %F A257063 Empirical for n mod 6 = 2: a(n) = (2/3)*n + (2/3) %F A257063 Empirical for n mod 6 = 3: a(n) = (2/3)*n + 1 %F A257063 Empirical for n mod 6 = 4: a(n) = (2/3)*n + (1/3) %F A257063 Empirical for n mod 6 = 5: a(n) = (2/3)*n + (2/3). %F A257063 Empirical g.f.: x*(1 + x + x^2 + x^4) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)). - _Colin Barker_, Dec 20 2018 %e A257063 All solutions for n=4: %e A257063 ..2....4....3 %Y A257063 Row 1 of A257062. %K A257063 nonn %O A257063 1,2 %A A257063 _R. H. Hardin_, Apr 15 2015