A223255 -id:A223255 - cp's OEIS frontend

A223249 Two-loop graph coloring a rectangular array: number of n X 2 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.

12, 52, 236, 1076, 4908, 22388, 102124, 465844, 2124972, 9693172, 44215916, 201693236, 920034348, 4196785268, 19143857644, 87325717684, 398340873132, 1817052930292, 8288582905196, 37808808665396, 172466877516588

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Column 2 of A223255.

			Some solutions for n=3:
..3..4....4..0....1..0....0..2....4..0....2..0....0..3....4..0....3..4....1..2
..4..0....0..2....0..4....3..0....0..2....0..2....2..0....0..4....4..0....0..1
..0..3....4..0....4..3....4..3....1..0....4..0....0..4....2..0....0..2....1..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A223255.

Empirical: a(n) = 5*a(n-1) - 2*a(n-2).
Conjectures from Colin Barker, Mar 16 2018: (Start)
G.f.: 4*x*(3 - 2*x) / (1 - 5*x + 2*x^2).
a(n) = (2^(1-n)*((5-sqrt(17))^n*(-1+sqrt(17)) + (1+sqrt(17))*(5+sqrt(17))^n)) / sqrt(17).
(End)

A223248 Two-loop graph coloring a rectangular array: number of n X n 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.

Original entry on oeis.org

5, 52, 2172, 307144, 200258884, 465277782336, 5036570504598960, 194136255385117730696, 34835929955107905273340132, 22243413468977139564311499153224, 66105120187260568220771918409079162896

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Diagonal of A223255

			Some solutions for n=3
..0..1..0....1..0..1....0..3..0....4..0..2....3..0..2....3..0..3....4..0..2
..3..0..2....0..2..0....2..0..3....0..1..0....0..4..0....0..4..0....0..2..1
..4..3..0....3..0..1....0..3..0....1..0..4....4..0..4....3..0..3....2..0..2

R. H. Hardin, Table of n, a(n) for n = 1..12

A223250 Two-loop graph coloring a rectangular array: number of n X 3 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.

Original entry on oeis.org

32, 236, 2172, 17828, 166892, 1382228, 12894316, 107283636, 996653548, 8326150836, 77047324460, 646086687220, 5957011569772, 50127570610868, 460630428892844, 3888717399278196, 35622664419652844, 301636706357260340

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Column 3 of A223255.

			Some solutions for n=3:
..3..0..1....4..0..3....3..4..3....1..0..4....4..3..4....1..0..3....1..0..3
..0..2..0....0..2..0....4..3..4....0..1..0....0..4..3....0..1..0....0..2..0
..4..0..2....2..0..3....3..4..0....3..0..2....3..0..4....3..0..1....2..0..2

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 2*a(n-1) +75*a(n-2) -126*a(n-3) -70*a(n-4) +48*a(n-5).

Empirical g.f.: -4*x*(78*x^4 -46*x^3 -175*x^2 +43*x +8) / (48*x^5 -70*x^4 -126*x^3 +75*x^2 +2*x -1). - Colin Barker, May 03 2014

A223251 Two-loop graph coloring a rectangular array: number of n X 4 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.

Original entry on oeis.org

80, 1076, 17828, 307144, 5359892, 93770308, 1641741608, 28748561780, 503440061060, 8816254627208, 154390919319636, 2703707386173764, 47347570829880040, 829155025056272692, 14520239405020681988

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Column 4 of A223255.

			Some solutions for n=3:
..4..0..4..3....2..0..3..0....0..4..0..2....0..3..0..1....3..0..3..0
..0..4..3..4....0..3..0..3....2..0..2..0....1..0..4..0....0..3..0..4
..1..0..4..3....3..0..2..0....0..3..0..1....0..4..0..4....4..0..2..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A223255.

Empirical: a(n) = 20*a(n-1) - 28*a(n-2) - 299*a(n-3) + 436*a(n-4) + 476*a(n-5) - 460*a(n-6) for n>7.

Empirical g.f.: 4*x*(20 - 131*x - 363*x^2 + 1158*x^3 + 760*x^4 - 1036*x^5 + 24*x^6) / (1 - 20*x + 28*x^2 + 299*x^3 - 436*x^4 - 476*x^5 + 460*x^6). - Colin Barker, Aug 18 2018

A223252 Two-loop graph coloring a rectangular array: number of nX5 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.

Original entry on oeis.org

208, 4908, 166892, 5359892, 200258884, 6581646956, 247417877452, 8146965446276, 306270743418628, 10089859264898796, 379171102402141516, 12496512099428874724, 469428050069027239844, 15477220252232343414028

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 5 of A223255

			Some solutions for n=3
..1..0..4..0..4....1..2..0..1..0....0..1..0..3..4....1..0..3..0..3
..0..2..0..4..0....2..0..3..0..2....2..0..2..0..3....0..3..0..2..0
..4..0..2..0..4....0..2..0..2..0....0..1..0..2..0....1..0..1..0..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 7*a(n-1) +1287*a(n-2) -8754*a(n-3) -66498*a(n-4) +293943*a(n-5) +1110271*a(n-6) -2420678*a(n-7) -6380827*a(n-8) +7393360*a(n-9) +14420088*a(n-10) -8685630*a(n-11) -12202500*a(n-12) +3405276*a(n-13) +3205824*a(n-14) -279936*a(n-15) -165888*a(n-16)

A223253 Two-loop graph coloring a rectangular array: number of nX6 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.

Original entry on oeis.org

528, 22388, 1382228, 93770308, 6581646956, 465277782336, 32969186423292, 2337308796813336, 165726502883851820, 11751198778793357708, 833253057095552710328, 59084372484837842357680, 4189562192845318714550284

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 6 of A223255

			Some solutions for n=3
..1..0..4..0..1..2....1..0..2..1..2..0....0..1..2..0..3..0....0..1..0..4..3..0
..0..3..0..4..0..1....0..2..0..2..0..3....1..2..0..3..0..4....1..0..4..3..0..4
..1..0..1..0..4..0....2..0..3..0..3..0....2..0..3..0..1..0....0..1..0..4..3..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 85*a(n-1) -629*a(n-2) -31878*a(n-3) +383553*a(n-4) +1511513*a(n-5) -30275140*a(n-6) +13466360*a(n-7) +868562158*a(n-8) -1847634768*a(n-9) -9913428815*a(n-10) +32760286161*a(n-11) +38433165015*a(n-12) -223138155283*a(n-13) +39999637275*a(n-14) +633199628532*a(n-15) -503848981336*a(n-16) -699539358490*a(n-17) +910162467392*a(n-18) +144242579620*a(n-19) -523191556820*a(n-20) +110096749408*a(n-21) +74380599616*a(n-22) -21347917248*a(n-23) -1345719744*a(n-24) for n>25

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.

Original entry on oeis.org

1360, 102124, 12894316, 1641741608, 247417877452, 32969186423292, 5036570504598960, 673319614527382164, 102954418641601279556, 13767068137991538439984, 2105133349737437751454452

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 7 of A223255

			Some solutions for n=3
..0..1..0..2..0..4..0....0..1..0..3..0..4..3....0..1..0..4..0..2..1
..1..0..2..0..2..0..1....1..0..4..0..4..3..0....1..0..2..0..1..0..2
..0..2..0..3..0..1..2....0..2..0..4..3..0..3....0..3..0..1..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210

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)

cp's OEIS Frontend

A223249 Two-loop graph coloring a rectangular array: number of n X 2 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.

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A223248 Two-loop graph coloring a rectangular array: number of n X n 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.

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A223250 Two-loop graph coloring a rectangular array: number of n X 3 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.

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A223251 Two-loop graph coloring a rectangular array: number of n X 4 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.

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A223252 Two-loop graph coloring a rectangular array: number of nX5 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.

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A223253 Two-loop graph coloring a rectangular array: number of nX6 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.

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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.

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