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 A189450 #8 May 02 2018 09:23:14 %S A189450 1,5,16,61,225,841,3136,11705,43681,163021,608400,2270581,8473921, %T A189450 31625105,118026496,440480881,1643897025,6135107221,22896531856, %U A189450 85451020205,318907548961,1190179175641,4441809153600,16577057438761 %N A189450 Number of 2 X n array permutations with each element moving zero or one space horizontally or diagonally. %C A189450 Row 2 of A189449. %H A189450 R. H. Hardin, <a href="/A189450/b189450.txt">Table of n, a(n) for n = 1..200</a> %F A189450 Empirical: a(n) = 4*a(n-1) -4*a(n-3) +a(n-4). %F A189450 Conjectures from _Colin Barker_, May 02 2018: (Start) %F A189450 G.f.: x*(1 + x - 4*x^2 + x^3) / ((1 - x)*(1 + x)*(1 - 4*x + x^2)). %F A189450 a(n) = ((2-sqrt(3))^(n+1) + (2+sqrt(3))^(n+1) + 8) / 12 for n even. %F A189450 a(n) = (-2+(2-sqrt(3))^(1+n) + (2+sqrt(3))^(1+n)) / 12 for n odd. %F A189450 (End) %e A189450 Some solutions for 2 X 3: %e A189450 ..4..5..2....0..5..2....0..1..2....1..0..2....0..2..1....0..1..2....4..2..1 %e A189450 ..3..0..1....3..4..1....4..3..5....4..3..5....3..4..5....3..4..5....3..0..5 %Y A189450 Cf. A189449. %K A189450 nonn %O A189450 1,2 %A A189450 _R. H. Hardin_, Apr 22 2011