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Rolling icosahedron face footprints: number of nX7 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge
1

%I #4 Mar 19 2013 08:06:31

%S 729,29943,1881441,137621799,10801441521,879050854455,72981761306721,

%T 6127190749734087,517631500569076305,43882777288012073559,

%U 3727442176083442555713,316954431035692378210023

%N Rolling icosahedron face footprints: number of nX7 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge

%C Column 7 of A223282

%H R. H. Hardin, <a href="/A223281/b223281.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 193*a(n-1) -13138*a(n-2) +389164*a(n-3) -4361048*a(n-4) -16478976*a(n-5) +680367552*a(n-6) -2205737728*a(n-7) -32395676672*a(n-8) +159364997888*a(n-9) +669407522304*a(n-10) -3582601411584*a(n-11) -5951537518592*a(n-12) +34040410587136*a(n-13) +16838602686464*a(n-14) -137580342149120*a(n-15) +18193951227904*a(n-16) +210744868077568*a(n-17) -92999396622336*a(n-18) -80015240724480*a(n-19) +37572373905408*a(n-20)

%e Some solutions for n=3

%e ..0..1..0..2..3..4..3....0..1..0..2..8..2..0....0..1..4..3.16..3.16

%e ..0..1..0..2..3..4.17....0..5..0..2..0..2..3....0..1..4..3..2..3..2

%e ..0..1..0..2..3..4..1....0..5..0..2..8..2..8....0..1..4..3..2..8..2

%e Face neighbors:

%e 0 -> 1 2 5

%e 1 -> 0 4 6

%e 2 -> 0 3 8

%e 3 -> 2 4 16

%e 4 -> 3 1 17

%e 5 -> 0 7 9

%e 6 -> 1 7 10

%e 7 -> 6 5 11

%e 8 -> 2 9 13

%e 9 -> 8 5 14

%e 10 -> 6 12 17

%e 11 -> 7 12 14

%e 12 -> 11 10 19

%e 13 -> 8 15 16

%e 14 -> 9 11 15

%e 15 -> 14 13 19

%e 16 -> 3 13 18

%e 17 -> 4 10 18

%e 18 -> 16 17 19

%e 19 -> 15 18 12

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 19 2013