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A223281 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.

%I A223281 #6 Jul 23 2025 03:57:18
%S A223281 729,29943,1881441,137621799,10801441521,879050854455,72981761306721,
%T A223281 6127190749734087,517631500569076305,43882777288012073559,
%U A223281 3727442176083442555713,316954431035692378210023
%N A223281 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 A223281 Column 7 of A223282
%H A223281 R. H. Hardin, <a href="/A223281/b223281.txt">Table of n, a(n) for n = 1..210</a>
%F A223281 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 A223281 Some solutions for n=3
%e A223281 ..0..1..0..2..3..4..3....0..1..0..2..8..2..0....0..1..4..3.16..3.16
%e A223281 ..0..1..0..2..3..4.17....0..5..0..2..0..2..3....0..1..4..3..2..3..2
%e A223281 ..0..1..0..2..3..4..1....0..5..0..2..8..2..8....0..1..4..3..2..8..2
%e A223281 Face neighbors:
%e A223281 0 -> 1 2 5
%e A223281 1 -> 0 4 6
%e A223281 2 -> 0 3 8
%e A223281 3 -> 2 4 16
%e A223281 4 -> 3 1 17
%e A223281 5 -> 0 7 9
%e A223281 6 -> 1 7 10
%e A223281 7 -> 6 5 11
%e A223281 8 -> 2 9 13
%e A223281 9 -> 8 5 14
%e A223281 10 -> 6 12 17
%e A223281 11 -> 7 12 14
%e A223281 12 -> 11 10 19
%e A223281 13 -> 8 15 16
%e A223281 14 -> 9 11 15
%e A223281 15 -> 14 13 19
%e A223281 16 -> 3 13 18
%e A223281 17 -> 4 10 18
%e A223281 18 -> 16 17 19
%e A223281 19 -> 15 18 12
%K A223281 nonn
%O A223281 1,1
%A A223281 _R. H. Hardin_ Mar 19 2013