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 A233162 #21 May 31 2024 09:22:16 %S A233162 1,1,3,11,48,236,1248,6896,39168,226496,1325568,7821056,46399488, %T A233162 276294656,1649369088,9862639616,59041579008,353712521216, %U A233162 2120127479808,12712174616576,76238687305728,457294683570176,2743218342985728 %N A233162 Number of n X 1 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabeled 8-colorings with no clashing color pairs). %C A233162 Column 1 of A233168. %H A233162 R. H. Hardin, <a href="/A233162/b233162.txt">Table of n, a(n) for n = 1..210</a> %H A233162 J. R. Britnell and M. Wildon, <a href="http://arxiv.org/abs/1507.04803">Bell numbers, partition moves and the eigenvalues of the random-to-top shuffle in types A, B and D</a>, arXiv 1507.04803 [math.CO], 2015. [I assume the connection mentioned in this paper will mean that the "Empirical" comment in the recurrence could be removed. - _N. J. A. Sloane_, Feb 27 2016] %F A233162 Empirical: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3) for n>4. %F A233162 Conjectures from _Colin Barker_, Feb 18 2018: (Start) %F A233162 G.f.: x*(1 - 11*x + 35*x^2 - 29*x^3) / ((1 - 2*x)*(1 - 4*x)*(1 - 6*x)). %F A233162 a(n) = (2^(n-6)*(90 + 9*2^n + 2*3^n)) / 9 for n>1. (End) %e A233162 Some solutions for n=5: %e A233162 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 %e A233162 ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1 %e A233162 ..7....7....2....0....2....2....2....2....2....7....2....2....7....0....2....0 %e A233162 ..6....2....6....2....6....7....1....7....7....1....6....0....2....1....6....2 %e A233162 ..7....0....3....6....7....3....2....5....1....2....2....6....6....7....0....1 %Y A233162 Cf. A233168. %K A233162 nonn %O A233162 1,3 %A A233162 _R. H. Hardin_, Dec 05 2013