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A223273 Rolling cube footprints: number of 5Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

%I A223273 #6 Jul 23 2025 03:56:51
%S A223273 1296,82944,27951104,6467616768,1771674009600,450204914417664,
%T A223273 118579442837618688,30710179999458000896,8018710224241441112064,
%U A223273 2085564910060985598869504,543463000691877698475130880
%N A223273 Rolling cube footprints: number of 5Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.
%C A223273 Row 5 of A223269
%H A223273 R. H. Hardin, <a href="/A223273/b223273.txt">Table of n, a(n) for n = 1..210</a>
%F A223273 Empirical: a(n) = 192*a(n-1) +31744*a(n-2) -3178496*a(n-3) -170917888*a(n-4) +13992198144*a(n-5) +99857989632*a(n-6) -17660905521152*a(n-7) +211106232532992*a(n-8) +2533274790395904*a(n-9) -40532396646334464*a(n-10) for n>11
%e A223273 Some solutions for n=3
%e A223273 ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
%e A223273 ..0..3..4....0..3..1....0..3..0....0..3..1....0..3..0....0..3..0....0..3..0
%e A223273 ..0..3..1....1..3..0....1..2..5....5..3..5....0..4..5....5..3..4....5..1..0
%e A223273 ..1..3..5....0..3..1....1..2..1....5..2..0....5..1..5....0..2..4....5..2..0
%e A223273 ..0..2..5....5..3..4....1..2..0....0..2..0....5..3..5....5..3..4....0..4..0
%e A223273 Face neighbors:
%e A223273 0.->.1.2.3.4
%e A223273 1.->.0.2.3.5
%e A223273 2.->.0.1.4.5
%e A223273 3.->.0.1.4.5
%e A223273 4.->.0.3.2.5
%e A223273 5.->.1.3.4.2
%K A223273 nonn
%O A223273 1,1
%A A223273 _R. H. Hardin_ Mar 19 2013