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Rolling icosahedron footprints: number of 5Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge
1

%I #5 Mar 19 2013 11:36:50

%S 20736,1953125,446265625,101966340125,24143758634125,5759605530667625,

%T 1379464144963464625,330817503041200989125,79372689616849936523125,

%U 19046505898852803312046625,4570642727979496865778147625

%N Rolling icosahedron footprints: number of 5Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge

%C Row 5 of A223321

%H R. H. Hardin, <a href="/A223325/b223325.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 410*a(n-1) -51839*a(n-2) +2998354*a(n-3) -88929070*a(n-4) +1198807214*a(n-5) +2889121905*a(n-6) -340756682572*a(n-7) +4538793109678*a(n-8) -13887817317962*a(n-9) -242674670034177*a(n-10) +2612400275589524*a(n-11) -4250937817051838*a(n-12) -72579353969012690*a(n-13) +404852006352195731*a(n-14) +294243010726671144*a(n-15) -8038059311698199807*a(n-16) +14527240098893219908*a(n-17) +63207106281330811172*a(n-18) -241285400707856322796*a(n-19) -99441316590244134158*a(n-20) +1499939986936247507922*a(n-21) -1264768034332853154292*a(n-22) -3709575277042038429058*a(n-23) +6249708500546392632287*a(n-24) +1712083980241985550010*a(n-25) -7806673210840206689815*a(n-26) +1552725322135658220450*a(n-27) +3587994096679078794377*a(n-28) -1272290169371896871744*a(n-29) -473135759143977735225*a(n-30) +224855787210470741790*a(n-31) -20543329382473731600*a(n-32) for n>36

%e Some solutions for n=3

%e ..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0

%e ..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0

%e ..0..5..7....0..5..7....0..6..5....0..1..0....0..7..3....0..5.10....0..7..0

%e ..0..5..6...10.11..7....4..6..5....0..6..5...11..9..4...10..6..0....1..7..1

%e ..6..0..7....5.11.10...10..6..0....4..6..0...10..9..8....0..1..7...11..3..9

%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 19 2013