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A223184 Rolling icosahedron footprints: number of nX6 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.

%I A223184 #6 Jul 23 2025 03:49:47
%S A223184 3125,5120,56960,738720,10117600,141047120,1978496760,27809548920,
%T A223184 391129835720,5502120113200,77403634963000,1088923059178480,
%U A223184 15319126239416880,215511834396404680,3031854469386423040
%N A223184 Rolling icosahedron footprints: number of nX6 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.
%C A223184 Column 6 of A223186
%H A223184 R. H. Hardin, <a href="/A223184/b223184.txt">Table of n, a(n) for n = 1..210</a>
%F A223184 Empirical: a(n) = 34*a(n-1) -485*a(n-2) +4346*a(n-3) -28802*a(n-4) +150848*a(n-5) -636337*a(n-6) +2159092*a(n-7) -5838756*a(n-8) +12438350*a(n-9) -20709448*a(n-10) +27153588*a(n-11) -29621182*a(n-12) +31551558*a(n-13) -39983024*a(n-14) +57518400*a(n-15) -77018236*a(n-16) +86977128*a(n-17) -80388139*a(n-18) +58849554*a(n-19) -31645539*a(n-20) +11534636*a(n-21) -3954177*a(n-22) +4130000*a(n-23) -5090133*a(n-24) +4343740*a(n-25) -2741059*a(n-26) +1290058*a(n-27) -452154*a(n-28) +127180*a(n-29) -31889*a(n-30) +7256*a(n-31) -1428*a(n-32) +212*a(n-33) -16*a(n-34) for n>37
%e A223184 Some solutions for n=3
%e A223184 ..0..5..7..1..2..8....0..7..5..0..7..5....0..1..2..0..1..7....0..2..1..3..7.11
%e A223184 ..7.11..3..8..1..2....1..0..7..1..0..7....2..0..1..2..0..1....1..0..7..1..3..7
%e A223184 ..3..7..1..3..8..4....7..1..0..7..5..0....6..2..8..1..7..3....7..1..0..7.11..5
%e A223184 Vertex neighbors:
%e A223184 0 -> 1 2 5 6 7
%e A223184 1 -> 0 2 3 7 8
%e A223184 2 -> 0 1 4 6 8
%e A223184 3 -> 1 7 8 9 11
%e A223184 4 -> 2 6 8 9 10
%e A223184 5 -> 0 6 7 10 11
%e A223184 6 -> 0 2 4 5 10
%e A223184 7 -> 0 1 3 5 11
%e A223184 8 -> 1 2 3 4 9
%e A223184 9 -> 3 4 8 10 11
%e A223184 10 -> 4 5 6 9 11
%e A223184 11 -> 3 5 7 9 10
%K A223184 nonn
%O A223184 1,1
%A A223184 _R. H. Hardin_ Mar 18 2013