A223556 -id:A223556 - cp's OEIS frontend

A223551 Petersen graph (3,1) coloring a rectangular array: number of n X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

1, 27, 3249, 1795473, 4715559621, 59043582882099, 3541866135681593043, 1020092567883788131348995, 1412857454503152706541498629089, 9420448274769727958157865214329990383

Offset: 1

R. H. Hardin Mar 22 2013

nonn

Diagonal of A223556

			Some solutions for n=3
..0..1..4....0..3..4....0..3..4....0..3..0....0..3..4....0..2..0....0..3..4
..0..3..0....5..3..4....5..3..0....5..3..4....5..3..4....0..2..1....4..5..4
..0..2..1....4..5..2....4..3..4....4..3..0....0..3..0....5..4..1....4..1..2

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

A223552 Petersen graph (3,1) coloring a rectangular array: number of n X 4 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

27, 1089, 44217, 1795473, 72906921, 2960456193, 120212193177, 4881332621169, 198211242377097, 8048559615522273, 326819564358379641, 13270825184845208913, 538874719548919491177, 21881530298548175795649

Offset: 1

R. H. Hardin, Mar 22 2013

nonn

Column 4 of A223556.

			Some solutions for n=3:
..0..2..0..2....0..1..2..5....0..2..0..2....0..2..1..4....0..1..0..1
..0..1..0..2....2..1..4..5....1..2..0..2....5..4..5..2....2..1..2..1
..4..1..0..2....4..3..4..5....5..3..5..4....5..2..1..0....4..1..4..3

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

Cf. A223556.

Empirical: a(n) = 41*a(n-1) - 16*a(n-2).
Conjectures from Colin Barker, Aug 21 2018: (Start)
G.f.: 9*x*(3 - 2*x) / (1 - 41*x + 16*x^2).
a(n) = 3*sqrt(3/11)*2^(-4-n)*((41-7*sqrt(33))^n*(-1+sqrt(33)) + (1+sqrt(33))*(41+7*sqrt(33))^n).
(End)

A223553 Petersen graph (3,1) coloring a rectangular array: number of n X 5 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

81, 6939, 609309, 53599905, 4715559621, 414863325945, 36498667573629, 3211064180380305, 282501632829717621, 24853807982558115945, 2186577702401491603629, 192369799106697718450305

Offset: 1

R. H. Hardin, Mar 22 2013

nonn

Column 5 of A223556.

			Some solutions for n=3:
..0..2..5..3..0....0..1..0..1..4....0..2..1..4..5....0..2..0..3..0
..0..2..5..2..1....0..1..2..5..3....0..2..1..4..1....0..2..0..2..5
..1..4..1..2..1....2..1..2..0..1....1..4..1..2..0....1..2..1..2..0

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

Cf. A223556.

Empirical: a(n) = 95*a(n-1) - 626*a(n-2) + 720*a(n-3) for n>4.

Empirical g.f.: 9*x*(9 - 84*x + 90*x^2 + 116*x^3) / (1 - 95*x + 626*x^2 - 720*x^3). - Colin Barker, Aug 21 2018

A223554 Petersen graph (3,1) coloring a rectangular array: number of nX6 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

243, 44217, 8410671, 1609602003, 308267930115, 59043582882099, 11308909481307639, 2166053304537606339, 414875312906229086427, 79463200007529976606227, 15219994937262513427990431

Offset: 1

R. H. Hardin Mar 22 2013

nonn

Column 6 of A223556

			Some solutions for n=3
..0..1..0..3..0..1....0..1..0..1..0..3....0..1..0..1..4..5....0..1..0..1..4..5
..0..1..0..1..4..1....0..1..0..3..0..3....0..1..2..5..4..1....0..1..2..5..2..5
..0..1..2..1..2..5....4..3..0..3..0..2....2..5..4..5..4..3....2..5..2..5..3..5

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

Empirical: a(n) = 229*a(n-1) -7630*a(n-2) +89386*a(n-3) -465129*a(n-4) +1124537*a(n-5) -1178896*a(n-6) +505856*a(n-7) -65536*a(n-8) for n>9

A223555 Petersen graph (3,1) coloring a rectangular array: number of nX7 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

729, 281763, 116124291, 48435199821, 20248676896077, 8468395670690901, 3541866135681593043, 1481382428937450207651, 619587781032925818024165, 259142468285816914838504985, 108386290103616110374877972691

Offset: 1

R. H. Hardin Mar 22 2013

nonn

Column 7 of A223556

			Some solutions for n=3
..0..1..0..3..0..3..4....0..1..0..3..5..4..1....0..1..0..1..0..3..5
..0..1..0..2..0..3..0....0..1..0..2..1..4..5....0..1..0..2..5..4..1
..0..3..0..1..4..1..4....0..3..5..2..5..4..3....0..3..0..3..5..2..1

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

Empirical: a(n) = 579*a(n-1) -77474*a(n-2) +4635156*a(n-3) -154699059*a(n-4) +3198735625*a(n-5) -43344055546*a(n-6) +396489063452*a(n-7) -2477765391092*a(n-8) +10544713088920*a(n-9) -29940917775104*a(n-10) +54099319050624*a(n-11) -56116354684928*a(n-12) +25386144890880*a(n-13) for n>15

A223557 Petersen graph (3,1) coloring a rectangular array: number of 2 X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

6, 27, 171, 1089, 6939, 44217, 281763, 1795473, 11441259, 72906921, 464583411, 2960456193, 18864859707, 120212193177, 766025913411, 4881332621169, 31105224694539, 198211242377097, 1263057797861523, 8048559615522273

Offset: 1

R. H. Hardin, Mar 22 2013

nonn

Row 2 of A223556.

			Some solutions for n=3:
..0..1..0....0..3..4....0..1..0....0..1..0....0..1..0....0..2..1....0..3..0
..0..2..5....4..5..2....0..3..0....0..2..1....0..1..0....1..2..1....4..1..4

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

Cf. A223556.

Empirical: a(n) = 7*a(n-1) - 4*a(n-2) for n>3.

Empirical g.f.: 3*x*(2 - x)*(1 - 2*x) / (1 - 7*x + 4*x^2). - Colin Barker, Aug 21 2018

A223558 Petersen graph (3,1) coloring a rectangular array: number of 3 X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

36, 243, 3249, 44217, 609309, 8410671, 116124291, 1603350909, 22137868197, 305663255847, 4220371688499, 58271764766661, 804573346481541, 11108952552823119, 153384184751908707, 2117815160357837997

Offset: 1

R. H. Hardin, Mar 22 2013

nonn

Row 3 of A223556.

			Some solutions for n=3:
..0..2..0....0..3..0....0..1..4....0..3..4....0..3..5....0..1..2....0..1..0
..5..2..5....5..2..1....2..5..3....0..3..4....5..4..3....2..5..4....4..3..5
..5..3..5....5..4..3....4..5..2....0..3..4....3..0..3....2..1..4....0..3..4

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

Cf. A223556.

Empirical: a(n) = 17*a(n-1) - 47*a(n-2) + 41*a(n-3) - 10*a(n-4) for n>6.

Empirical g.f.: 9*x*(4 - 41*x + 90*x^2 - 119*x^3 + 80*x^4 - 18*x^5) / ((1 - x)*(1 - 16*x + 31*x^2 - 10*x^3)). - Colin Barker, Aug 21 2018

A223559 Petersen graph (3,1) coloring a rectangular array: number of 4Xn 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

216, 2187, 61731, 1795473, 53599905, 1609602003, 48435199821, 1458216189189, 43906852932615, 1322067596579721, 39808646082180639, 1198675626234407289, 36093255426614169063, 1086802077561066049509, 32724639445955516294571

Offset: 1

R. H. Hardin Mar 22 2013

nonn

Row 4 of A223556

			Some solutions for n=3
..0..3..5....0..1..2....0..3..4....0..1..0....0..1..4....0..1..4....0..3..5
..5..3..0....4..1..2....0..1..2....4..1..4....4..5..2....4..1..4....5..2..5
..4..1..0....2..5..4....4..1..2....2..5..2....4..5..2....4..1..4....5..4..5
..2..1..4....4..5..4....2..5..2....2..0..3....3..0..2....4..1..0....1..2..5

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

Empirical: a(n) = 48*a(n-1) -663*a(n-2) +4174*a(n-3) -13683*a(n-4) +22624*a(n-5) -11071*a(n-6) -19190*a(n-7) +27600*a(n-8) -3924*a(n-9) -10466*a(n-10) +4220*a(n-11) +556*a(n-12) -224*a(n-13) for n>16

A223560 Petersen graph (3,1) coloring a rectangular array: number of 5Xn 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

1296, 19683, 1172889, 72906921, 4715559621, 308267930115, 20248676896077, 1332349841732589, 87722782781246325, 5776909246026951831, 380457710460248943159, 25056802652197918165101, 1650241268196778787267997

Offset: 1

R. H. Hardin Mar 22 2013

nonn

Row 5 of A223556

			Some solutions for n=3
..0..1..0....0..1..0....0..1..0....0..1..0....0..2..0....0..1..0....0..2..0
..0..1..4....0..2..5....0..1..0....0..3..0....0..3..4....0..1..2....0..2..1
..4..5..4....1..2..0....2..1..2....4..3..0....0..1..0....2..1..4....1..4..3
..2..1..0....0..1..4....2..5..3....0..1..4....4..1..4....4..3..0....1..4..5
..4..3..5....4..1..0....2..0..3....4..1..2....0..1..0....5..2..0....5..3..5

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

Empirical: a(n) = 138*a(n-1) -6973*a(n-2) +184648*a(n-3) -2923158*a(n-4) +28742148*a(n-5) -164862328*a(n-6) +323303482*a(n-7) +2664572505*a(n-8) -23705019366*a(n-9) +69355645652*a(n-10) +70054378686*a(n-11) -1192186614062*a(n-12) +3436488705480*a(n-13) -144865949345*a(n-14) -25285605346206*a(n-15) +67796388682571*a(n-16) -36846019769990*a(n-17) -198206747323771*a(n-18) +539872407671898*a(n-19) -524423165469667*a(n-20) -173098284258962*a(n-21) +1095810256049880*a(n-22) -1391226239663130*a(n-23) +883819140137974*a(n-24) -205123488401360*a(n-25) -109599889287411*a(n-26) +100027213354804*a(n-27) -24361114004738*a(n-28) -4709924309874*a(n-29) +4076735604787*a(n-30) -668752166416*a(n-31) -125749417451*a(n-32) +60592095948*a(n-33) -5244227851*a(n-34) -1102919206*a(n-35) +264396239*a(n-36) -12021054*a(n-37) -1712600*a(n-38) +222192*a(n-39) -8748*a(n-40) +108*a(n-41) for n>45

A223561 Petersen graph (3,1) coloring a rectangular array: number of 6Xn 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

Original entry on oeis.org

7776, 177147, 22284891, 2960456193, 414863325945, 59043582882099, 8468395670690901, 1218666102798243879, 175642608583999726713, 25331295128141837865681, 3654268425473611746796515

Offset: 1

R. H. Hardin Mar 22 2013

nonn

Row 6 of A223556

			Some solutions for n=3
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..0..3..0....0..1..0....0..3..0....0..3..0....0..3..0....0..3..0....0..1..0
..0..1..0....0..2..1....0..3..5....0..3..4....0..1..2....0..1..4....0..1..0
..0..1..0....0..2..0....0..3..0....0..3..4....2..0..2....2..1..0....2..1..0
..0..1..4....0..3..4....0..3..0....4..3..5....2..5..3....0..2..0....0..2..0
..2..5..3....0..3..0....5..2..1....5..4..1....3..4..3....0..3..0....0..2..5

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

cp's OEIS Frontend

A223551 Petersen graph (3,1) coloring a rectangular array: number of n X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223552 Petersen graph (3,1) coloring a rectangular array: number of n X 4 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223553 Petersen graph (3,1) coloring a rectangular array: number of n X 5 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223554 Petersen graph (3,1) coloring a rectangular array: number of nX6 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223555 Petersen graph (3,1) coloring a rectangular array: number of nX7 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223557 Petersen graph (3,1) coloring a rectangular array: number of 2 X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223558 Petersen graph (3,1) coloring a rectangular array: number of 3 X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223559 Petersen graph (3,1) coloring a rectangular array: number of 4Xn 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223560 Petersen graph (3,1) coloring a rectangular array: number of 5Xn 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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A223561 Petersen graph (3,1) coloring a rectangular array: number of 6Xn 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

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