A233174 -id:A233174 - cp's OEIS frontend

A233169 Number of n X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

1, 8, 2688, 7938048, 221463445504, 48667983827959808, 95229762257179140685824, 1517114635517382193142028042240, 212050285595421539693130354498977398784, 244891984772140151804896156943078190424499683328

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Diagonal of A233174

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

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

A233170 Number of n X 4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

Original entry on oeis.org

10, 800, 78336, 7938048, 808583168, 82428559360, 8403942375424, 856833627521024, 87359712110051328, 8906889846866313216, 908115313250288009216, 92588259810472408121344, 9439975016878714881310720

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

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

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

Column 4 of A233174.

Empirical: a(n) = 128*a(n-1) - 2816*a(n-2) + 16384*a(n-3).

Empirical g.f.: 2*x*(5 - 240*x + 2048*x^2) / ((1 - 16*x)*(1 - 112*x + 1024*x^2)). - Colin Barker, Oct 10 2018

A233171 Number of n X 5 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

Original entry on oeis.org

36, 8576, 2469888, 736362496, 221463445504, 66799223701504, 20170789919653888, 6093499625887498240, 1841146791439003287552, 556341623248212690206720, 168115390615337809829953536, 50801739257391729644354404352

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

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

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

Column 5 of A233174.

Empirical: a(n) = 480*a(n-1) -60416*a(n-2) +1966080*a(n-3) +22020096*a(n-4) -1845493760*a(n-5) +22548578304*a(n-6) -68719476736*a(n-7)

A233172 Number of nX6 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

136, 92672, 76447744, 65265467392, 56275748519936, 48667983827959808, 42129429039341895680, 36480870847649836695552, 31592958742989872646062080, 27360904144981190573706706944, 23696028949244230878346703011840

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Column 6 of A233174

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

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

Empirical: a(n) = 1216*a(n-1) -303104*a(n-2) -6553600*a(n-3) +6056574976*a(n-4) -287762808832*a(n-5) -18622978195456*a(n-6) +1482141674242048*a(n-7) -15199648742375424*a(n-8) -522417556774977536*a(n-9) +5764607523034234880*a(n-10)

A233173 Number of nX7 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

528, 1009664, 2385772544, 5896922988544, 14822434649669632, 37512454919740719104, 95229762257179140685824, 242105801211204186752942080, 615953046875285234718796152832

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Column 7 of A233174

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

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

Empirical: a(n) = 5376*a(n-1) -9666560*a(n-2) +6641680384*a(n-3) -514859204608*a(n-4) -1288661987491840*a(n-5) +418421348973412352*a(n-6) +37913553463018520576*a(n-7) -32422674725335864442880*a(n-8) +2456986406781633163165696*a(n-9) +743294581445578569579233280*a(n-10) -127145448531964683219491618816*a(n-11) -541734166879150708735933939712*a(n-12) +1458065585310949453860586897014784*a(n-13) -105361096550619343762748861090627584*a(n-14) +324477988839219423442308126073683968*a(n-15) +230584711190673160155410811484335243264*a(n-16) -7433042952429249561278089081087686868992*a(n-17) -29094142371740238626118528935416182079488*a(n-18) +4137833581758611715714635226370301451304960*a(n-19) -44601490397061246283071436545296723011960832*a(n-20)

A233175 Number of 2 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

3, 8, 80, 800, 8576, 92672, 1009664, 11018240, 120356864, 1315045376, 14370209792, 157036838912, 1716116258816, 18754008252416, 204947383648256, 2239705722650624, 24475955615498240, 267478202279002112

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

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

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

Row 2 of A233174.

Empirical: a(n) = 12*a(n-1) - 128*a(n-3) for n>4.
Conjectures from Colin Barker, Oct 10 2018: (Start)
G.f.: x*(3 - 28*x - 16*x^2 + 224*x^3) / ((1 - 4*x)*(1 - 8*x - 32*x^2)).
a(n) = 2^(2*n-3) + (1/32)*sqrt(3)*(-(4-4*sqrt(3))^n + (4*(1+sqrt(3)))^n) for n>1.
(End)

A233176 Number of 3 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

11, 80, 2688, 78336, 2469888, 76447744, 2385772544, 74291609600, 2315406802944, 72144847372288, 2248141575290880, 70053467808333824, 2182930872087347200, 68021929516908675072, 2119621843032249204736, 66049216835347669843968

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

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

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

Row 3 of A233174.

Empirical: a(n) = 32*a(n-1) + 64*a(n-2) - 3072*a(n-3) + 8192*a(n-4) for n>5.

Empirical g.f.: x*(11 - 272*x - 576*x^2 + 20992*x^3 - 53248*x^4) / ((1 - 8*x)*(1 - 24*x - 256*x^2 + 1024*x^3)). - Colin Barker, Oct 10 2018

A233177 Number of 4Xn 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

Original entry on oeis.org

48, 896, 96256, 7938048, 736362496, 65265467392, 5896922988544, 528589678182400, 47540804020862976, 4269747110598934528, 383704462840431640576, 34473222428763411709952, 3097514921527666217582592

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Row 4 of A233174

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

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

Empirical: a(n) = 64*a(n-1) +3328*a(n-2) -77824*a(n-3) -1441792*a(n-4) +28311552*a(n-5) +33554432*a(n-6) -1073741824*a(n-7) for n>8

A233178 Number of 5Xn 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

236, 10496, 3497984, 808583168, 221463445504, 56275748519936, 14822434649669632, 3838772637371203584, 1002338782428226650112, 260695613898360688214016, 67932875090988311936761856

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Row 5 of A233174

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

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

A233179 Number of 6Xn 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

Original entry on oeis.org

1248, 124928, 127533056, 82428559360, 66799223701504, 48667983827959808, 37512454919740719104, 28097680435284371570688, 21372669849836167383482368, 16126697116955385553150279680, 12221294273626033135123316080640

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Row 6 of A233174

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

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

Empirical: a(n) = 448*a(n-1) +421888*a(n-2) -95682560*a(n-3) -48586817536*a(n-4) +7696581394432*a(n-5) +2219020623282176*a(n-6) -331924968239529984*a(n-7) -45544058606667694080*a(n-8) +7676565708838105251840*a(n-9) +384720682715267981115392*a(n-10) -90389119748153097756606464*a(n-11) -732939612340266155036901376*a(n-12) +559176850836005482125888323584*a(n-13) -7028965514623047698676841447424*a(n-14) -1887473560557987165955670813966336*a(n-15) +44169859058027396737075939400220672*a(n-16) +3500683050361467360162023730212503552*a(n-17) -101555160700421718306247628235154128896*a(n-18) -3466958920006006825501354764976208740352*a(n-19) +108207134224866861549607317549181730553856*a(n-20) +1701156622829501613469275506203267231121408*a(n-21) -52659376845749069097884147249280994259238912*a(n-22) -315694924216699133847365011797178367569035264*a(n-23) +9366312983382861719445001674512311832511774720*a(n-24) for n>25

cp's OEIS Frontend

A233169 Number of n X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233170 Number of n X 4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

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A233171 Number of n X 5 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

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A233172 Number of nX6 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233173 Number of nX7 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233175 Number of 2 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233176 Number of 3 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233177 Number of 4Xn 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabeled 6-colorings with no clashing color pairs).

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A233178 Number of 5Xn 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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A233179 Number of 6Xn 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

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