|
%I #4 Mar 18 2013 20:31:55
%S 3125,753005,236027705,78951770585,27049155640325,9343721361109325,
%T 3237164242739054345,1122694859942471556185,389510525064654891088085,
%U 135155431698699358247850605,46899472272729726654991007705
%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, diagonal or antidiagonal neighbor moves along an icosahedral edge
%C Column 6 of A223233
%H R. H. Hardin, <a href="/A223231/b223231.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 525*a(n-1) -66702*a(n-2) +1331899*a(n-3) +153275287*a(n-4) -7341587858*a(n-5) +30374971203*a(n-6) +3824146236752*a(n-7) -75111050134232*a(n-8) +205037655577424*a(n-9) +6460684913361019*a(n-10) -49290095118307364*a(n-11) -140021336623195442*a(n-12) +2200689678890462843*a(n-13) -1458667313500165314*a(n-14) -37187688159845953965*a(n-15) +75037715810598760272*a(n-16) +230357416636661884542*a(n-17) -652626536223111303870*a(n-18) -496313838990773846658*a(n-19) +2029968756189631881972*a(n-20) +256192718593072185252*a(n-21) -2481072401873869960176*a(n-22) +64389835845560317824*a(n-23) +1236374401394896182000*a(n-24) -45277328877999388704*a(n-25) -205116615409293840384*a(n-26)
%e Some solutions for n=3
%e ..0..6..0..5..6.10....0..6..0..1..0..1....0..6..4..2..0..2....0..6..0..2..0..2
%e ..0..6..0..5..6..5....0..6..0..1..0..5....0..6..0..2..0..7....0..6..0..7..0..7
%e ..0..6..0..5..6..2....0..6..0..1..7..1....0..6..0..7..1..7....0..6..0..2..0..2
%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
| 