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A223236 Rolling icosahedron footprints: number of 4Xn 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.

%I A223236 #6 Jul 23 2025 03:54:15
%S A223236 1728,10985,812225,32837285,1697263985,78951770585,3843057179285,
%T A223236 183367303999865,8826695677742465,423223089093370325,
%U A223236 20328307272501475145,975647469218575594625,46842159188887320714725
%N A223236 Rolling icosahedron footprints: number of 4Xn 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 A223236 Row 4 of A223233
%H A223236 R. H. Hardin, <a href="/A223236/b223236.txt">Table of n, a(n) for n = 1..210</a>
%F A223236 Empirical: a(n) = 32*a(n-1) +1042*a(n-2) -11074*a(n-3) -125832*a(n-4) +1314816*a(n-5) -820893*a(n-6) -14900218*a(n-7) +19327896*a(n-8) +41119416*a(n-9) -33578064*a(n-10) -26034048*a(n-11) +12597120*a(n-12) for n>13
%e A223236 Some solutions for n=3
%e A223236 ..0..6.10....0..6..0....0..6..4....0..6.10....0..6.10....0..6..2....0..6..0
%e A223236 ..4..6..4....0..7..0....4..6..2...10..6..0....4..6..0....0..6..2....4..6..0
%e A223236 ..5..6..2....3..7..1....5..6..0....4..6..4....5..6..2....2..6..4....2..6..4
%e A223236 ..5..0..2....5..7..3....5..6..0....5.10..5....2..6..0....5..6..0...10..6..4
%e A223236 Vertex neighbors:
%e A223236 0 -> 1 2 5 6 7
%e A223236 1 -> 0 2 3 7 8
%e A223236 2 -> 0 1 4 6 8
%e A223236 3 -> 1 7 8 9 11
%e A223236 4 -> 2 6 8 9 10
%e A223236 5 -> 0 6 7 10 11
%e A223236 6 -> 0 2 4 5 10
%e A223236 7 -> 0 1 3 5 11
%e A223236 8 -> 1 2 3 4 9
%e A223236 9 -> 3 4 8 10 11
%e A223236 10 -> 4 5 6 9 11
%e A223236 11 -> 3 5 7 9 10
%K A223236 nonn
%O A223236 1,1
%A A223236 _R. H. Hardin_ Mar 18 2013