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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
1

%I #4 Mar 18 2013 05:17:25

%S 3125,5120,56960,738720,10117600,141047120,1978496760,27809548920,

%T 391129835720,5502120113200,77403634963000,1088923059178480,

%U 15319126239416880,215511834396404680,3031854469386423040

%N 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 Column 6 of A223186

%H R. H. Hardin, <a href="/A223184/b223184.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Some solutions for n=3

%e ..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 ..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 ..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 Vertex neighbors:

%e 0 -> 1 2 5 6 7

%e 1 -> 0 2 3 7 8

%e 2 -> 0 1 4 6 8

%e 3 -> 1 7 8 9 11

%e 4 -> 2 6 8 9 10

%e 5 -> 0 6 7 10 11

%e 6 -> 0 2 4 5 10

%e 7 -> 0 1 3 5 11

%e 8 -> 1 2 3 4 9

%e 9 -> 3 4 8 10 11

%e 10 -> 4 5 6 9 11

%e 11 -> 3 5 7 9 10

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 18 2013