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 A245990 #13 Mar 25 2025 19:55:34 %S A245990 28,68,164,396,956,2308,5572,13452,32476,78404,189284,456972,1103228, %T A245990 2663428,6430084,15523596,37477276,90478148,218433572,527345292, %U A245990 1273124156,3073593604,7420311364,17914216332,43248744028,104411704388 %N A245990 Number of length n+2 0..3 arrays with no pair in any consecutive three terms totalling exactly 3. %H A245990 R. H. Hardin, <a href="/A245990/b245990.txt">Table of n, a(n) for n = 1..210</a> %F A245990 Empirical: a(n) = 2*a(n-1) + a(n-2). %F A245990 Conjectures from _Colin Barker_, Nov 05 2018: (Start) %F A245990 G.f.: 4*x*(7 + 3*x) / (1 - 2*x - x^2). %F A245990 a(n) = sqrt(2)*((1-sqrt(2))^n*(-4+3*sqrt(2)) + (1+sqrt(2))^n*(4+3*sqrt(2))). %F A245990 (End) %e A245990 Some solutions for n=10: %e A245990 3 2 1 1 2 1 1 2 0 2 3 0 1 3 3 0 %e A245990 3 2 1 0 2 3 0 2 2 3 2 0 3 1 2 2 %e A245990 3 3 3 0 3 1 0 2 0 2 2 0 1 1 2 0 %e A245990 3 2 1 1 3 1 0 2 0 3 2 1 3 3 3 2 %e A245990 3 3 1 1 1 1 0 0 0 3 0 1 1 1 3 2 %e A245990 2 3 0 0 3 3 2 2 1 2 2 1 1 3 2 2 %e A245990 2 2 1 0 1 1 2 2 1 3 0 1 1 3 2 2 %e A245990 2 3 1 1 3 3 3 2 1 3 2 0 3 3 3 0 %e A245990 3 3 1 1 3 1 3 2 3 3 0 0 1 2 2 0 %e A245990 2 1 0 3 3 1 2 3 3 2 2 0 1 3 2 1 %e A245990 3 1 0 1 3 0 3 3 2 2 2 0 0 3 3 1 %e A245990 2 0 1 3 3 0 2 1 3 0 3 1 0 1 2 3 %Y A245990 Column 3 of A245995. %Y A245990 Essentially 4 times A001333. %K A245990 nonn %O A245990 1,1 %A A245990 _R. H. Hardin_, Aug 09 2014