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%I #4 Mar 19 2013 12:07:23
%S 262144,1594323,771895089,373714754427,181703507374179,
%T 88422165323034669,43041050285035823937,20952806226803446547979,
%U 10200311867482640569384803,4965790918632215208497280621,2417489227433689564468440912057
%N Rolling cube footprints: number of 7Xn 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge
%C Row 7 of A223331
%H R. H. Hardin, <a href="/A223336/b223336.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 1017*a(n-1) -381153*a(n-2) +76330925*a(n-3) -9379669404*a(n-4) +747532248534*a(n-5) -38499863181596*a(n-6) +1139954614587576*a(n-7) -5583055176706479*a(n-8) -1094431324506682925*a(n-9) +50537184076461725934*a(n-10) -1015258431965719361244*a(n-11) +3095570263329310857414*a(n-12) +351032728024216265247750*a(n-13) -8715911720129630011302099*a(n-14) +67896300297745233456034095*a(n-15) +862567216416574756707869697*a(n-16) -25376301969118851499248569685*a(n-17) +189481741633620976743863445870*a(n-18) +1213881680830549398947848361250*a(n-19) -33701546470498136557101837454170*a(n-20) +193817191950113071661498477713494*a(n-21) +1105391498469154893964681382128230*a(n-22) -21334493200414307906998488358434330*a(n-23) +79226547906556204139213650387509229*a(n-24) +554852186342095607470419069220373331*a(n-25) -6242703657785811406542257712875475819*a(n-26) +11427072259363660331384127096122658759*a(n-27) +130251581424149170693623570641906239872*a(n-28) -791454998632744644019698078348974703252*a(n-29) +150183001780574465288696031737669683446*a(n-30) +13021503011401984451434439252140174731984*a(n-31) -39238347770704076075162550684665356370931*a(n-32) -54363423267461595132483159664169706700377*a(n-33) +511583255147743885153317284758744493422968*a(n-34) -611466515286479680979853300688193412132840*a(n-35) -2288068847976359716858330082703129157497324*a(n-36) +7143935107773190831122804291852527329425180*a(n-37) -646497305327209377732210692074196271867879*a(n-38) -24260350279666085911492453378468843083738153*a(n-39) +31366989158217866691843797464920854600869029*a(n-40) +18403204408585929605908614199621520086661637*a(n-41) -72616510295082242362026374686186931457144498*a(n-42) +46505758190559990385450468895760155088783636*a(n-43) +28528493644475533596840131207619521026564086*a(n-44) -60080596653327296067550212394399506018872694*a(n-45) +38580578456372532586316733205323399729445890*a(n-46) -12050175487651135339486502499983588770170012*a(n-47) +1509805849627288567831603949640808080305292*a(n-48) +117034612538436236819170072080398495133180*a(n-49) -52192142460391429881159477398798743239984*a(n-50) +4001693815102511240259579194781596297544*a(n-51) for n>57
%e Some solutions for n=3
%e ..0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0
%e ..0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0
%e ..0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0
%e ..0..4..6....0..4..5....0..2..6....0..4..0....0..2..0....0..2..3....6..2..6
%e ..5..4..5....6..4..5....0..2..6....0..4..5....3..1..5....6..2..6....6..7..3
%e ..6..4..6....5..1..5....6..2..6....5..4..6....3..1..3....6..2..0....3..2..3
%e ..6..4..0....3..7..5....6..2..0....6..2..0....3..2..3....3..2..6....3..7..3
%e Vertex neighbors:
%e 0 -> 1 2 4
%e 1 -> 0 3 5
%e 2 -> 0 3 6
%e 3 -> 1 2 7
%e 4 -> 0 5 6
%e 5 -> 1 4 7
%e 6 -> 2 4 7
%e 7 -> 3 5 6
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 19 2013
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