A233202 -id:A233202 - cp's OEIS frontend

A233196 Number of n X 2 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabeled 8-colorings with no clashing color pairs).

1, 3, 36, 528, 8256, 131328, 2098176, 33558528, 536887296, 8590000128, 137439215616, 2199024304128, 35184376283136, 562949970198528, 9007199321849856, 144115188344291328, 2305843010287435776

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

			Some solutions for n=5:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....2..3....2..0....2..3....2..0....2..7....2..0....2..7....2..3....2..0
..7..1....0..2....3..6....1..0....3..6....6..3....3..1....6..2....7..6....3..6
..4..0....3..7....2..4....3..1....0..2....5..7....2..4....3..1....3..5....7..5
..6..4....1..4....1..0....5..3....3..7....3..1....0..2....0..5....7..4....3..0

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

Column 2 of A233202.

Empirical: a(n) = 20*a(n-1) - 64*a(n-2) for n>3.
Conjectures from Colin Barker, Oct 10 2018: (Start)
G.f.: x*(1 - 17*x + 40*x^2) / ((1 - 4*x)*(1 - 16*x)).
a(n) = 2^(2*n-7) * (4^n+8) for n>1.
(End)

A233197 Number of n X 3 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

3, 36, 1440, 62720, 2779136, 123551744, 5496242176, 244533166080, 10879798083584, 484067845865472, 21537343823413248, 958248525617954816, 42634797465737363456, 1896925413514655301632, 84398806858761213313024

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

			Some solutions for n=4:
..0..1..7....0..1..2....0..1..0....0..1..2....0..1..2....0..1..2....0..1..2
..2..3..1....3..0..1....2..3..1....3..7..6....5..7..6....3..7..1....5..3..7
..7..2..0....2..3..7....6..0..5....1..5..4....6..5..3....2..4..2....0..5..1
..3..6..2....7..5..1....3..6..0....4..6..5....0..1..0....7..1..7....3..7..2

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

Column 3 of A233202.

Empirical: a(n) = 64*a(n-1) - 960*a(n-2) + 4096*a(n-3) for n>4.

Empirical g.f.: x*(3 - 156*x + 2016*x^2 - 7168*x^3) / ((1 - 8*x)*(1 - 56*x + 512*x^2)). - Colin Barker, Oct 10 2018

A233198 Number of n X 4 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

11, 528, 62720, 7802880, 981532672, 123833679872, 15635845218304, 1974688792182784, 249403601212932096, 31500304517060100096, 3978590250109478371328, 502509651344957204594688

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

			Some solutions for n=3:
..0..1..2..0....0..1..2..6....0..1..2..3....0..1..2..3....0..1..0..2
..2..0..3..5....3..0..4..5....2..0..6..2....2..3..6..5....3..2..1..4
..6..5..1..7....1..2..1..4....1..5..7..3....6..5..3..0....6..3..5..6

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

Column 4 of A233202.

Empirical: a(n) = 208*a(n-1) - 13312*a(n-2) + 442368*a(n-3) - 8650752*a(n-4) + 67108864*a(n-5) for n>6.

Empirical g.f.: x*(11 - 1760*x + 99328*x^2 - 3080192*x^3 + 55050240*x^4 - 369098752*x^5) / ((1 - 16*x)*(1 - 192*x + 10240*x^2 - 278528*x^3 + 4194304*x^4)). - Colin Barker, Oct 10 2018

A233199 Number of nX5 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

48, 8256, 2779136, 981532672, 352524959744, 127365174788096, 46111939268444160, 16706602064729341952, 6054323596680792899584, 2194196637563524913037312, 795235812066308877870694400

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Column 5 of A233202

			Some solutions for n=2
..0..1..2..3..0....0..1..2..1..3....0..1..2..3..5....0..1..2..0..3
..5..3..0..5..4....4..0..3..0..1....3..7..1..0..1....4..0..3..6..2

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

Empirical: a(n) = 736*a(n-1) -203776*a(n-2) +33062912*a(n-3) -3665821696*a(n-4) +270851375104*a(n-5) -10685878632448*a(n-6) -116548232544256*a(n-7) +35184372088832000*a(n-8) -1423137482249076736*a(n-9) +18446744073709551616*a(n-10) for n>11

A233200 Number of n X 6 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

236, 131328, 123551744, 123833679872, 127365174788096, 132364161848967168, 138127371171167993856, 144372294092575012290560, 150991906277433156745297920, 157951736213079507379343589376

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Column 6 of A233202.

			Some solutions for n=2
..0..1..0..1..0..2....0..1..2..6..3..2....0..1..2..7..6..2....0..1..2..1..3..1
..3..2..3..2..6..3....2..0..4..2..0..6....2..0..6..5..3..0....2..4..0..2..7..2

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

Cf. A233202.

Empirical: a(n) = 2624*a(n-1) -2916352*a(n-2) +2023751680*a(n-3) -1022873305088*a(n-4) +396210733056000*a(n-5) -117075448369774592*a(n-6) +24978582014512857088*a(n-7) -3235719238675389743104*a(n-8) +32228191279027496943616*a(n-9) +79127659192314522138312704*a(n-10) -14330945495506960134011092992*a(n-11) +573127552562903399144703918080*a(n-12) +175763191005253023447780744495104*a(n-13) -41436012082310191504073111849926656*a(n-14) +7185129802334419767282615543889133568*a(n-15) -1237277610717122610430160500786185895936*a(n-16) +170446905899499762382455179339748584980480*a(n-17) -17499361001276181422067502561786112042336256*a(n-18) +1430383734999503249937564429831586312219525120*a(n-19) -95447189449711067045772874206934987245596180480*a(n-20) +4407340875076004112707987073660040981149921574912*a(n-21) -93536104789177786765035829293842113257979682750464*a(n-22) for n > 23.

A233201 Number of nX7 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

1248, 2098176, 5496242176, 15635845218304, 46111939268444160, 138127371171167993856, 416547612309880393695232, 1259808519497450508966166528, 3814894993577338604838516162560

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Column 7 of A233202

			Some solutions for n=2
..0..1..0..2..6..5..0....0..1..0..2..6..3..7....0..1..0..2..7..3..2
..3..2..6..3..7..1..3....3..2..6..3..5..1..4....2..4..6..4..2..6..4

R. H. Hardin, Table of n, a(n) for n = 1..101

A233195 Number of n X n 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

Original entry on oeis.org

1, 3, 1440, 7802880, 352524959744, 132364161848967168, 416547612309880393695232, 11042955940877644659574580445184, 2474201164323675429580723288914257772544

Offset: 1

R. H. Hardin, Dec 05 2013

nonn

Diagonal of A233202

			Some solutions for n=3
..0..1..2....0..1..2....0..1..2....0..1..7....0..1..0....0..1..2....0..1..2
..5..0..6....5..0..6....2..3..7....2..3..1....2..3..5....3..0..1....5..7..3
..6..5..3....3..5..7....6..5..4....1..7..4....6..7..3....1..2..3....4..2..0

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