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 A183721 #11 Apr 04 2018 10:48:01 %S A183721 0,1,12,87,537,3070,16731,88331,455804,2311983,11571209,57295330, %T A183721 281223411,1370286715,6635743136,31964799247,153273890393, %U A183721 732031932806,3483896304443,16529018119643,78202676604548,369073777749215 %N A183721 1/12 the number of (n+1) X 2 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction. %C A183721 Column 1 of A183729. %H A183721 R. H. Hardin, <a href="/A183721/b183721.txt">Table of n, a(n) for n = 1..200</a> %F A183721 Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 23*a(n-3) + 6*a(n-4) + 7*a(n-5) - 2*a(n-6). %F A183721 Empirical g.f.: x^2*(1 + 2*x - x^2)^2 / ((1 + x)*(1 - 5*x + 2*x^2)*(1 - 4*x - 2*x^2 + x^3)). - _Colin Barker_, Apr 04 2018 %e A183721 All solutions with the first block increasing clockwise for 3 X 2: %e A183721 ..3..4....1..2....4..5....2..3....5..0....0..1 %e A183721 ..2..5....0..3....3..0....1..4....4..1....5..2 %e A183721 ..1..0....5..4....2..1....0..5....3..2....4..3 %e A183721 ... %e A183721 ...R.......R.......R.......R.......R.......R... %e A183721 ...R.......R.......R.......R.......R.......R... %Y A183721 Cf. A183729. %K A183721 nonn %O A183721 1,3 %A A183721 _R. H. Hardin_, Jan 06 2011