A223269 -id:A223269 - cp's OEIS frontend

A223264 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

1, 48, 20992, 63438848, 1771674009600, 389343801904201728, 761838097494483172065280, 12136917084120610801062514786304, 1696402284763369899693403606733469777920

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Diagonal of A223269

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

R. H. Hardin, Table of n, a(n) for n = 1..14

A223265 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

64, 6144, 622592, 63438848, 6467616768, 659411697664, 67231270567936, 6854664725200896, 698877628160933888, 71255117675418877952, 7264922488410118029312, 740706078202304288260096

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 4 of A223269.

			Some solutions for n=3:
..0..3..5..1....0..4..2..0....0..3..0..1....0..3..5..2....0..3..4..3
..0..3..5..2....0..4..2..0....0..1..0..3....0..2..0..3....0..2..0..2
..0..2..1..2....0..4..3..4....0..1..0..4....0..3..5..3....1..2..1..2
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Cf. A223269.

Empirical: a(n) = 112*a(n-1) - 1024*a(n-2).

Empirical g.f.: 64*x*(1 - 16*x) / (1 - 112*x + 1024*x^2). - Colin Barker, Aug 18 2018

A223266 Rolling cube footprints: number of n X 5 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

256, 67584, 19726336, 5889851392, 1771674009600, 534392715870208, 161366284997492736, 48747995907588358144, 14729174296327654211584, 4450732984859801614811136, 1344923124886673681620664320

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 5 of A223269.

			Some solutions for n=3:
..0..3..5..2..5....0..3..5..4..3....0..3..5..2..1....0..3..5..3..5
..0..3..5..1..5....0..3..0..4..2....0..3..1..3..4....0..3..4..3..5
..0..3..0..4..0....0..1..0..1..2....0..3..1..2..4....0..3..1..3..1
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Cf. A223269.

Empirical: a(n) = 448*a(n-1) -46080*a(n-2) +491520*a(n-3) +37748736*a(n-4) -637534208*a(n-5) +2147483648*a(n-6).

A223267 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

1024, 737280, 611319808, 522106961920, 450204914417664, 389343801904201728, 337035427916688654336, 291846966499723716853760, 252743669925904582659014656, 218887233158696603085046808576

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Column 6 of A223269

			Some solutions for n=3
..0..3..0..2..1..3....0..3..0..2..4..2....0..3..0..2..0..2....0..3..0..2..1..3
..0..3..0..2..0..2....0..3..0..2..4..2....0..3..0..1..5..1....0..3..0..3..0..2
..0..3..0..4..5..1....0..3..0..3..1..3....0..3..0..4..3..4....0..3..0..2..5..1
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Empirical: a(n) = 1152*a(n-1) -229376*a(n-2) -21233664*a(n-3) +4697620480*a(n-4) +12884901888*a(n-5) -17798344474624*a(n-6) +343047627866112*a(n-7) +6755399441055744*a(n-8) -90071992547409920*a(n-9)

A223268 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

4096, 8060928, 19084083200, 47175115472896, 118579442837618688, 300099634959879241728, 761838097494483172065280, 1936846409617575899985608704, 4927624374993058505713514446848

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Column 7 of A223269

			Some solutions for n=3
..0..3..0..3..0..2..0....0..3..0..3..4..3..4....0..3..0..3..1..2..4
..0..3..0..3..5..4..5....0..3..0..3..5..2..5....0..3..0..3..0..2..5
..0..3..0..4..5..4..2....0..3..0..1..0..2..1....0..3..0..3..1..2..1
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Empirical: a(n) = 5248*a(n-1) -8994816*a(n-2) +5490343936*a(n-3) +187904819200*a(n-4) -1264610170634240*a(n-5) +256551247132229632*a(n-6) +70752113095943913472*a(n-7) -23366404249055043518464*a(n-8) -533913337097412407197696*a(n-9) +674953674297109781457928192*a(n-10) -40751378221934631192876810240*a(n-11) -5757910579286783501424165650432*a(n-12) +721053031162241165678293693759488*a(n-13) -13066308561852474555927268289413120*a(n-14) -1348009507077897319716382214971195392*a(n-15) +58039494284702303231713887968022233088*a(n-16) -3987683987354747618711421180841033728*a(n-17) -29604565922121646321313590846563834396672*a(n-18) +348449143727040986586495598010130648530944*a(n-19)

A223270 Rolling cube footprints: number of 2 X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

6, 48, 576, 6144, 67584, 737280, 8060928, 88080384, 962592768, 10519314432, 114957484032, 1256277934080, 13728862961664, 150031797583872, 1639577995444224, 17917641486237696, 195807627744116736

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 2 of A223269.

			Some solutions for n=3:
..0..2..0....0..2..1....0..3..4....0..2..4....0..2..0....0..1..2....0..4..2
..5..3..4....4..3..1....4..2..4....1..3..1....1..3..5....2..4..3....0..1..0
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Cf. A223269.

Empirical: a(n) = 8*a(n-1) + 32*a(n-2).
Conjectures from Colin Barker, Aug 18 2018: (Start)
G.f.: 6*x / (1 - 8*x - 32*x^2).
a(n) = (sqrt(3)*(-(4-4*sqrt(3))^n + (4*(1+sqrt(3)))^n)) / 4.
(End)

A223271 Rolling cube footprints: number of 3 X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

36, 576, 20992, 622592, 19726336, 611319808, 19084083200, 594316099584, 18523120205824, 577157705236480, 17985124012392448, 560427673747193856, 17463446426942963712, 544175431737222889472, 16956974709073621549056

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 3 of A223269.

			Some solutions for n=3:
..0..2..5....0..2..1....0..1..0....0..1..0....0..1..5....0..2..0....0..1..5
..0..2..0....4..3..1....0..3..0....5..3..5....0..1..0....5..1..0....0..3..5
..4..3..4....0..2..1....0..4..5....4..2..0....2..4..3....0..3..5....5..3..1
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Cf. A223269.

Empirical: a(n) = 24*a(n-1) + 256*a(n-2) - 1024*a(n-3) for n>4.

Empirical g.f.: 4*x*(9 - 72*x - 512*x^2 + 2048*x^3) / (1 - 24*x - 256*x^2 + 1024*x^3). - Colin Barker, Aug 18 2018

A223272 Rolling cube footprints: number of 4Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

216, 6912, 765952, 63438848, 5889851392, 522106961920, 47175115472896, 4228713130491904, 380326363447427072, 34157975785279848448, 3069635685131267080192, 275785779148632316968960

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 4 of A223269

			Some solutions for n=3
..0..3..0....0..3..0....0..3..0....0..3..0....0..3..1....0..3..1....0..3..0
..0..2..1....4..2..5....0..4..0....5..4..0....1..3..4....4..2..4....5..2..0
..4..2..5....1..3..5....5..3..5....2..4..5....1..3..5....4..3..5....1..3..5
..4..2..4....5..2..5....5..3..5....2..4..2....5..2..0....4..2..4....4..3..4
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Empirical: a(n) = 48*a(n-1) +4096*a(n-2) -12288*a(n-3) -1638400*a(n-4) +2097152*a(n-5) +67108864*a(n-6) for n>7

A223273 Rolling cube footprints: number of 5Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

1296, 82944, 27951104, 6467616768, 1771674009600, 450204914417664, 118579442837618688, 30710179999458000896, 8018710224241441112064, 2085564910060985598869504, 543463000691877698475130880

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 5 of A223269

			Some solutions for n=3
..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
..0..3..4....0..3..1....0..3..0....0..3..1....0..3..0....0..3..0....0..3..0
..0..3..1....1..3..0....1..2..5....5..3..5....0..4..5....5..3..4....5..1..0
..1..3..5....0..3..1....1..2..1....5..2..0....5..1..5....0..2..4....5..2..0
..0..2..5....5..3..4....1..2..0....0..2..0....5..3..5....5..3..4....0..4..0
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Empirical: a(n) = 192*a(n-1) +31744*a(n-2) -3178496*a(n-3) -170917888*a(n-4) +13992198144*a(n-5) +99857989632*a(n-6) -17660905521152*a(n-7) +211106232532992*a(n-8) +2533274790395904*a(n-9) -40532396646334464*a(n-10) for n>11

A223274 Rolling cube footprints: number of 6Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

7776, 995328, 1020002304, 659411697664, 534392715870208, 389343801904201728, 300099634959879241728, 224781443200799995854848, 170981358780674940558376960, 129013576934490162920595390464

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 6 of A223269

			Some solutions for n=3
..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
..0..3..1....0..3..1....0..3..4....0..3..0....0..3..0....0..3..0....0..3..0
..1..2..4....4..3..0....0..3..1....0..2..5....1..3..5....4..2..4....4..3..1
..0..2..4....0..2..0....5..3..5....0..4..5....0..3..0....4..2..4....0..3..4
..4..3..5....0..4..0....1..2..5....5..2..0....5..1..5....5..2..5....0..3..0
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2

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

Empirical: a(n) = 384*a(n-1) +446464*a(n-2) -67108864*a(n-3) -52881784832*a(n-4) +4312147165184*a(n-5) +2494998041853952*a(n-6) -172245093560877056*a(n-7) -56567744594563825664*a(n-8) +4056230054786020409344*a(n-9) +644319406221573287313408*a(n-10) -49152677749972407368548352*a(n-11) -3878710988338500226623995904*a(n-12) +310939347582341467621952585728*a(n-13) +12871152730646806229128124039168*a(n-14) -1063719785796591567291470875459584*a(n-15) -23908207232954463569578196629192704*a(n-16) +1970557787452381691709019145944170496*a(n-17) +24560537696530709963129597105272782848*a(n-18) -1895084507428041387861060550238750638080*a(n-19) -13078274250527787273500557666098310283264*a(n-20) +864147070795723227965239815572975372992512*a(n-21) +2646035685177217491891200947389429612281856*a(n-22) -146348640365357214366328151164254872382996480*a(n-23) for n>24

cp's OEIS Frontend

A223264 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223265 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223266 Rolling cube footprints: number of n X 5 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223267 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223268 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223270 Rolling cube footprints: number of 2 X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223271 Rolling cube footprints: number of 3 X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223272 Rolling cube footprints: number of 4Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223273 Rolling cube footprints: number of 5Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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A223274 Rolling cube footprints: number of 6Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

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