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 A223278 #8 Aug 18 2018 11:23:25 %S A223278 27,351,4995,72279,1048923,15229647,221142771,3211159815,46628577099, %T A223278 677084057343,9831800199267,142765577323191,2073070007320635, %U A223278 30102629340815919,437114178530327763,6347246378746198887 %N A223278 Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge. %C A223278 Column 4 of A223282. %H A223278 R. H. Hardin, <a href="/A223278/b223278.txt">Table of n, a(n) for n = 1..210</a> %F A223278 Empirical: a(n) = 17*a(n-1) - 36*a(n-2). %F A223278 Conjectures from _Colin Barker_, Aug 18 2018: (Start) %F A223278 G.f.: 27*x*(1 - 4*x) / (1 - 17*x + 36*x^2). %F A223278 a(n) = (3*2^(-1-n)*((17-sqrt(145))^n*(-1+sqrt(145)) + (1+sqrt(145))*(17+sqrt(145))^n)) / sqrt(145). %F A223278 (End) %e A223278 Some solutions for n=3: %e A223278 ..0..2..3.16....0..2..0..1....0..1..0..1....0..2..0..1....0..5..0..1 %e A223278 ..8..2..3..2....0..5..0..1....4..1..4..1....0..1..0..5....0..2..0..1 %e A223278 ..3..2..3.16....7..5..0..5....4..1..6..1....4..1..0..5....3..2..0..5 %e A223278 Face neighbors: %e A223278 0 -> 1 2 5 %e A223278 1 -> 0 4 6 %e A223278 2 -> 0 3 8 %e A223278 3 -> 2 4 16 %e A223278 4 -> 3 1 17 %e A223278 5 -> 0 7 9 %e A223278 6 -> 1 7 10 %e A223278 7 -> 6 5 11 %e A223278 8 -> 2 9 13 %e A223278 9 -> 8 5 14 %e A223278 10 -> 6 12 17 %e A223278 11 -> 7 12 14 %e A223278 12 -> 11 10 19 %e A223278 13 -> 8 15 16 %e A223278 14 -> 9 11 15 %e A223278 15 -> 14 13 19 %e A223278 16 -> 3 13 18 %e A223278 17 -> 4 10 18 %e A223278 18 -> 16 17 19 %e A223278 19 -> 15 18 12 %Y A223278 Cf. A223282. %K A223278 nonn %O A223278 1,1 %A A223278 _R. H. Hardin_, Mar 19 2013