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A223320 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.

%I A223320 #6 Jul 23 2025 04:00:15
%S A223320 15625,46411625,142980696625,443803619416625,1379464144963464625,
%T A223320 4288761014162797342625,13334277936752000032650625,
%U A223320 41458126974532997739670258625,128899204399783389165401518452625
%N A223320 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 A223320 Column 7 of A223321
%H A223320 R. H. Hardin, <a href="/A223320/b223320.txt">Table of n, a(n) for n = 1..210</a>
%F A223320 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 A223320 Some solutions for n=3
%e A223320 ..0..6..0..6..0..1..2....0..6..0..6..0..1..2....0..6..0..6..0..6..2
%e A223320 ..0..6..0..6..0..1..3....0..6..0..6..2..6..5....0..6..0..6.10..6.10
%e A223320 ..0..6..0..7..3..7..1....0..6..0..6..4..6..4....0..6..0..6..5..6.10
%e A223320 Vertex neighbors:
%e A223320 0 -> 1 2 5 6 7
%e A223320 1 -> 0 2 3 7 8
%e A223320 2 -> 0 1 4 6 8
%e A223320 3 -> 1 7 8 9 11
%e A223320 4 -> 2 6 8 9 10
%e A223320 5 -> 0 6 7 10 11
%e A223320 6 -> 0 2 4 5 10
%e A223320 7 -> 0 1 3 5 11
%e A223320 8 -> 1 2 3 4 9
%e A223320 9 -> 3 4 8 10 11
%e A223320 10 -> 4 5 6 9 11
%e A223320 11 -> 3 5 7 9 10
%K A223320 nonn
%O A223320 1,1
%A A223320 _R. H. Hardin_ Mar 19 2013