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 A223254 Two-loop graph coloring a rectangular array: number of nX7 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph 1

%I

%S 1360,102124,12894316,1641741608,247417877452,32969186423292,

%T 5036570504598960,673319614527382164,102954418641601279556,

%U 13767068137991538439984,2105133349737437751454452

%N Two-loop graph coloring a rectangular array: number of nX7 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

%C Column 7 of A223255

%H R. H. Hardin, <a href="/A223254/b223254.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 28*a(n-1) +22094*a(n-2) -612638*a(n-3) -34697699*a(n-4) +857426087*a(n-5) +19269402083*a(n-6) -452582710450*a(n-7) -5196357651810*a(n-8) +121471255123047*a(n-9) +784521840286299*a(n-10) -19032823427395385*a(n-11) -71557106240148347*a(n-12) +1891596620100268189*a(n-13) +4053226562326676303*a(n-14) -125850760507130739816*a(n-15) -137325250302977363349*a(n-16) +5810206342561348221792*a(n-17) +2112063228796457766208*a(n-18) -190673412380784423155523*a(n-19) +31175977139208452841748*a(n-20) +4519088491717666637943212*a(n-21) -2521009426787393216157164*a(n-22) -78132441653059251312771506*a(n-23) +67194762786548095348886706*a(n-24) +991114633234547769096497383*a(n-25) -1086487065817112140135963239*a(n-26) -9246978111462053478444877636*a(n-27) +11886663585913058313103682788*a(n-28) +63437992765700926323675439626*a(n-29) -91549165616667691671986180456*a(n-30) -319096012027915093663208225978*a(n-31) +505270224709833483992343060812*a(n-32) +1169834119125926599000090452428*a(n-33) -2013976920409425274563378937984*a(n-34) -3093825797818422519435176190276*a(n-35) +5806901155448165023300226112840*a(n-36) +5802724403164614446962360484208*a(n-37) -12069185782933153870041272901536*a(n-38) -7498268619479233256865142564552*a(n-39) +17928562164912874429715500178360*a(n-40) +6324408946861809730655778612160*a(n-41) -18769551482877658743060850485888*a(n-42) -3062428455340820497880529989168*a(n-43) +13571071687302027627071236968416*a(n-44) +447339093913524148546448894816*a(n-45) -6594517197317653991928731489984*a(n-46) +334978098941260036945575132544*a(n-47) +2079714767979448381582777555328*a(n-48) -203584094318775781647563314944*a(n-49) -407780845143970783852048131072*a(n-50) +48290081689441182403407559680*a(n-51) +47082942851826200463302584320*a(n-52) -5861611427120503395946905600*a(n-53) -2969668429000649309135241216*a(n-54) +367509759847220125558112256*a(n-55) +87962023235261091708665856*a(n-56) -10576877402078797696598016*a(n-57) -778809194746098437062656*a(n-58) +91689031189590139994112*a(n-59)

%e Some solutions for n=3

%e ..0..1..0..2..0..4..0....0..1..0..3..0..4..3....0..1..0..4..0..2..1

%e ..1..0..2..0..2..0..1....1..0..4..0..4..3..0....1..0..2..0..1..0..2

%e ..0..2..0..3..0..1..2....0..2..0..4..3..0..3....0..3..0..1..0..1..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 18 2013

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)