A223202 -id:A223202 - cp's OEIS frontend

A223197 Rolling cube footprints: number of n X 3 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

16, 576, 20992, 765952, 27951104, 1020002304, 37222350848, 1358333739008, 49568888651776, 1808888827478016, 66010735351693312, 2408891644150546432, 87906291641005113344, 3207913535188934590464, 117064536077508729110528

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Column 3 of A223202.

			Some solutions for n=3:
..0..1..0....0..1..5....0..3..4....0..4..5....0..3..4....0..1..5....0..3..1
..2..0..3....2..5..2....1..0..2....1..5..1....3..0..2....1..2..1....3..4..3
..0..2..0....5..1..5....5..2..1....5..1..2....4..2..4....0..4..0....4..3..1
Face neighbors:
0,5 -> 1 2 3 4
1,4 -> 0 2 3 5
2,3 -> 0 1 4 5

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

Cf. A223202.

Empirical: a(n) = 40*a(n-1) - 128*a(n-2).
Conjectures from Colin Barker, Mar 16 2018: (Start)
G.f.: 16*x*(1 - 4*x) / (1 - 40*x + 128*x^2).
a(n) = ((20-4*sqrt(17))^n*(-3+sqrt(17)) + (3+sqrt(17))*(4*(5+sqrt(17)))^n) / (4*sqrt(17)).
(End)

A223196 Rolling cube footprints: number of n X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

Original entry on oeis.org

1, 48, 20992, 85327872, 3249109204992, 1163614255186968576, 3928452022261522225954816, 125206136723337854976992338771968, 37708401216116613420253652395390480154624

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Diagonal of A223202

			Some solutions for n=3
..0..2..4....0..2..0....0..1..5....0..3..4....0..3..5....0..3..5....0..1..0
..4..0..3....3..4..3....3..5..2....2..0..3....2..0..4....3..1..3....1..5..1
..3..1..0....5..2..0....1..2..4....0..1..5....5..1..2....1..3..1....0..4..0
Face neighbors:
0,5 -> 1 2 3 4
1,4 -> 0 2 3 5
2,3 -> 0 1 4 5

R. H. Hardin, Table of n, a(n) for n = 1..13

A223198 Rolling cube footprints: number of n X 4 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

Original entry on oeis.org

64, 6912, 765952, 85327872, 9515827200, 1061444124672, 118404195287040, 13208119651860480, 1473383170773614592, 164357898631630553088, 18334348775748242767872, 2045221757767217986928640

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Column 4 of A223202.

			Some solutions for n=3:
..0..2..5..2....0..3..5..3....0..3..1..3....0..1..0..2....0..2..4..5
..3..1..3..4....3..4..2..0....3..0..3..0....3..0..3..4....3..4..0..4
..1..3..4..2....1..5..1..2....4..2..0..1....0..3..5..2....1..0..1..0
Face neighbors:
0,5 -> 1 2 3 4
1,4 -> 0 2 3 5
2,3 -> 0 1 4 5

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

Cf. A223202.

Empirical: a(n) = 144*a(n-1) - 3840*a(n-2) + 24576*a(n-3).

Empirical g.f.: 64*x*(1 - 36*x + 256*x^2) / (1 - 144*x + 3840*x^2 - 24576*x^3). - Colin Barker, Aug 17 2018

A223199 Rolling cube footprints: number of nX5 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

Original entry on oeis.org

256, 82944, 27951104, 9515827200, 3249109204992, 1110327429169152, 379529320596504576, 129739120821684666368, 44351234892702995709952, 15161534293466127643181056, 5183001897895978479097217024

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 5 of A223202

			Some solutions for n=3
..0..3..0..3..1....0..3..0..3..4....0..3..0..1..2....0..3..4..3..0
..3..0..3..1..5....3..0..3..4..3....3..0..4..2..0....3..0..3..5..2
..0..1..5..3..1....0..3..4..2..1....0..1..0..4..2....0..3..1..2..1
Face neighbors:
0,5 -> 1 2 3 4
1,4 -> 0 2 3 5
2,3 -> 0 1 4 5

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

Empirical: a(n) = 512*a(n-1) -66560*a(n-2) +3014656*a(n-3) -50331648*a(n-4) +268435456*a(n-5)

A223200 Rolling cube footprints: number of nX6 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

Original entry on oeis.org

1024, 995328, 1020002304, 1061444124672, 1110327429169152, 1163614255186968576, 1220273386789986631680, 1280001086812985197854720, 1342770055307877057357152256, 1408661948573682047511982768128

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 6 of A223202

			Some solutions for n=3
..0..3..0..4..2..4....0..3..0..3..0..2....0..3..0..3..1..0....0..3..0..2..5..1
..3..0..3..5..1..5....3..0..3..5..2..1....3..0..3..0..3..4....3..0..3..0..1..0
..0..3..1..2..0..3....0..3..0..3..0..3....0..3..4..3..5..3....0..3..0..3..5..2
Face neighbors:
0,5 -> 1 2 3 4
1,4 -> 0 2 3 5
2,3 -> 0 1 4 5

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

Empirical: a(n) = 1920*a(n-1) -1191936*a(n-2) +335020032*a(n-3) -48670703616*a(n-4) +3778497478656*a(n-5) -147884313935872*a(n-6) +2269391999729664*a(n-7)

A223201 Rolling cube footprints: number of nX7 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

Original entry on oeis.org

4096, 11943936, 37222350848, 118404195287040, 379529320596504576, 1220273386789986631680, 3928452022261522225954816, 12653687328474521535529353216, 40767113911221149476183875780608

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 7 of A223202

			Some solutions for n=3
..0..3..0..3..1..3..5....0..3..0..3..0..3..1....0..3..0..3..0..2..0
..3..0..3..0..2..0..2....3..0..3..0..3..0..2....3..0..3..0..3..5..1
..0..3..0..3..4..3..0....0..3..0..3..0..3..5....0..3..0..4..0..1..0
Face neighbors:
0,5 -> 1 2 3 4
1,4 -> 0 2 3 5
2,3 -> 0 1 4 5

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

Empirical: a(n) = 7040*a(n-1) -18169856*a(n-2) +23760732160*a(n-3) -18040473255936*a(n-4) +8500736711196672*a(n-5) -2561598209927413760*a(n-6) +496452053123372941312*a(n-7) -61015776557932010799104*a(n-8) +4604307320797904083353600*a(n-9) -203533995411681708710297600*a(n-10) +5009788596483023299982393344*a(n-11) -63134942003554394019855335424*a(n-12) +316912650057057350374175801344*a(n-13)

cp's OEIS Frontend

A223197 Rolling cube footprints: number of n X 3 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

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A223196 Rolling cube footprints: number of n X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

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A223198 Rolling cube footprints: number of n X 4 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

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A223199 Rolling cube footprints: number of nX5 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

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A223200 Rolling cube footprints: number of nX6 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

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A223201 Rolling cube footprints: number of nX7 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

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Comments

Examples

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