A223357 -id:A223357 - cp's OEIS frontend

A223353 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 antidiagonal neighbor moves across a corresponding cube edge.

1, 64, 36864, 191102976, 9273505480704, 4204783428144463872, 17937911731045128424390656, 720606995188478656413544250081280, 273159296445528717756285371297713115627520

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Diagonal of A223357

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

R. H. Hardin, Table of n, a(n) for n = 1..15

A223354 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 or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

256, 110592, 48365568, 21177040896, 9273505480704, 4060947412942848, 1778325505192230912, 778744859776908263424, 341019436981212766273536, 149335504495574154699866112, 65395371895437880547981918208

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 5 of A223357.

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

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

Cf. A223357.

Empirical: a(n) = 480*a(n-1) - 18432*a(n-2).

Empirical g.f.: 256*x*(1 - 48*x) / (1 - 480*x + 18432*x^2). - Colin Barker, Aug 19 2018

A223355 Rolling cube footprints: number of n X 6 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

1024, 1327104, 1764753408, 2356125106176, 3147420753985536, 4204783428144463872, 5617417467128419713024, 7504647859211051911348224, 10025914758161450104466178048, 13394228581283493899583803621376

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 6 of A223357.

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

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

Cf. A223357.

Empirical: a(n) = 1600*a(n-1) - 368640*a(n-2) + 21233664*a(n-3).

Empirical g.f.: 1024*x*(1 - 304*x + 18432*x^2) / (1 - 1600*x + 368640*x^2 - 21233664*x^3). - Colin Barker, Aug 19 2018

A223356 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 antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

4096, 15925248, 64399343616, 262687716016128, 1073434373061083136, 4387933871654786039808, 17937911731045128424390656, 73331159360640809507160588288, 299782360886263133728989486514176

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Column 7 of A223357

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

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

Empirical: a(n) = 5376*a(n-1) -5750784*a(n-2) +2038431744*a(n-3) -217432719360*a(n-4)

A223358 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 or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

36, 1024, 36864, 1327104, 48365568, 1764753408, 64399343616, 2350085308416, 85760296353792, 3129600934674432, 114206719453691904, 4167679858509348864, 152088734250301390848, 5550086348122858979328, 202536095940875781144576

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 3 of A223357.

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

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

Cf. A223357.

Empirical: a(n) = 40*a(n-1) - 128*a(n-2) for n>4.

Empirical g.f.: 4*x*(9 - 104*x + 128*x^2 - 4096*x^3) / (1 - 40*x + 128*x^2). - Colin Barker, Aug 19 2018

A223359 Rolling cube footprints: number of 4 X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

216, 16384, 1769472, 191102976, 21177040896, 2356125106176, 262687716016128, 29299957655666688, 3268377203523452928, 364590293218429501440, 40670509521269453488128, 4536850283257824395919360

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 4 of A223357.

			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
..4..3..5....0..4..3....4..2..1....5..1..2....0..2..5....5..3..4....0..4..3
..4..2..4....0..4..2....5..3..1....0..1..3....0..2..0....0..3..1....2..5..1
..1..2..4....3..1..3....5..2..4....3..1..0....4..2..4....5..3..4....1..5..2

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

Cf. A223357.

Empirical: a(n) = 144*a(n-1) -3840*a(n-2) +24576*a(n-3) for n>7.

A223360 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 or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

1296, 262144, 84934656, 27518828544, 9273505480704, 3147420753985536, 1073434373061083136, 366633735578651197440, 125301697729353543057408, 42831316037653820665233408, 14641648774856138730026041344

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 5 of A223357

			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
..1..2..5....4..2..1....5..1..2....1..2..0....0..1..3....4..2..0....5..4..2
..1..2..1....0..2..1....2..0..4....5..4..3....0..1..2....1..2..5....5..4..2
..4..2..5....0..2..1....4..2..1....3..5..4....5..1..3....0..3..1....0..4..2

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

Empirical: a(n) = 512*a(n-1) -65536*a(n-2) +2490368*a(n-3) +17825792*a(n-4) -2818572288*a(n-5) +51539607552*a(n-6) -274877906944*a(n-7) for n>11

A223361 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 or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

7776, 4194304, 4076863488, 3962711310336, 4060947412942848, 4204783428144463872, 4387933871654786039808, 4591848540270748206366720, 4812465805493379433041494016, 5046647918221316806981151883264

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 6 of A223357

			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..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
..1..2..4....1..3..5....5..3..0....0..1..0....1..2..1....0..3..1....0..4..0
..1..2..1....5..4..3....0..3..1....2..4..0....1..0..4....4..3..1....0..2..0
..1..0..3....2..0..1....0..2..4....0..3..4....4..2..0....5..2..5....5..1..5

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

Empirical: a(n) = 1920*a(n-1) -1159168*a(n-2) +272105472*a(n-3) -9613344768*a(n-4) -7199438929920*a(n-5) +1446957302153216*a(n-6) -121544413380870144*a(n-7) +4845873199050653696*a(n-8) -74363437047141629952*a(n-9) for n>15

A223362 Rolling cube footprints: number of 7Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.

Original entry on oeis.org

46656, 67108864, 195689447424, 570630428688384, 1778325505192230912, 5617417467128419713024, 17937911731045128424390656, 57521864635406651506997329920, 184928520804269688527323467350016

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 7 of A223357

			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..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
..4..2..1....0..1..5....0..4..0....4..2..1....4..2..0....4..3..0....1..2..1
..1..0..2....5..1..5....5..2..4....4..2..0....5..1..0....0..4..2....0..2..1
..3..1..5....3..4..0....4..0..2....5..2..0....2..4..0....2..5..3....4..5..4

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

Empirical: a(n) = 7040*a(n-1) -17465344*a(n-2) +18800967680*a(n-3) -5309116448768*a(n-4) -7749529751257088*a(n-5) +8887216147871563776*a(n-6) -3856931134576087007232*a(n-7) +531878790929751511924736*a(n-8) +190513388777369932266471424*a(n-9) -93741331145837409444827234304*a(n-10) +12222651524429752285684779974656*a(n-11) +1263810026656038306032296239562752*a(n-12) -551654242165579114325543159492247552*a(n-13) +43085332629682837240804749191541686272*a(n-14) +4872287652438761570329355653127757365248*a(n-15) -1026508698180612029879031419004744959524864*a(n-16) +28871206910743184105746848222880083247890432*a(n-17) +6540175709583032206058076985272862827184390144*a(n-18) -575371596066692387006645352028057086492317581312*a(n-19) -2523619228901320906565606486887706533101261815808*a(n-20) +2349623641089498925710775976637864762211733222719488*a(n-21) -95152890975475098118298655640034501348474058126131200*a(n-22) -1267975436522094077386825701907323687325172579365289984*a(n-23) +199392037012347758180468057735634758937394385475357114368*a(n-24) -6056422377501992768232187451298021893661257010869595799552*a(n-25) +80033047126180179738906315145897746805305031916916440039424*a(n-26) -401734511064747568885490523085290650630550748445698208825344*a(n-27) for n>33

cp's OEIS Frontend

A223353 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 antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

A223354 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 or antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A223355 Rolling cube footprints: number of n X 6 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A223356 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 antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223358 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 or antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A223359 Rolling cube footprints: number of 4 X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A223360 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 or antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223361 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 or antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223362 Rolling cube footprints: number of 7Xn 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.

Views

Author

Keywords

Comments

Examples

Links

Formula