A223320 - OEIS

%I #4 Mar 19 2013 11:29:18

%S 15625,46411625,142980696625,443803619416625,1379464144963464625,

%T 4288761014162797342625,13334277936752000032650625,

%U 41458126974532997739670258625,128899204399783389165401518452625

%N Rolling icosahedron footprints: number of nX7 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 Column 7 of A223321

%H R. H. Hardin, <a href="/A223320/b223320.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4313*a(n-1) -4293540*a(n-2) +1835925129*a(n-3) -400542201531*a(n-4) +46506128233194*a(n-5) -2762797384141236*a(n-6) +72983536818080616*a(n-7) -643864107456947520*a(n-8)

%e Some solutions for n=3

%e ..0..6..0..6..0..1..2....0..6..0..6..0..1..2....0..6..0..6..0..6..2

%e ..0..6..0..6..0..1..3....0..6..0..6..2..6..5....0..6..0..6.10..6.10

%e ..0..6..0..7..3..7..1....0..6..0..6..4..6..4....0..6..0..6..5..6.10

%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