A206238 -id:A206238 - cp's OEIS frontend

A206230 Number of (n+1)X(n+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

15, 256, 4456, 283728, 10915392, 1448239080, 649065145152, 203396423662488, 222950396746461504, 842104767130879914696, 2305567526828592241306992, 22136848571138455592306188104, 737206270850592131066195723493312

Offset: 1

R. H. Hardin Feb 05 2012

nonn

Diagonal of A206238

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

R. H. Hardin, Table of n, a(n) for n = 1..16

A206231 Number of (n+1) X 2 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

Original entry on oeis.org

15, 60, 310, 1640, 8910, 51066, 294546, 1710184, 10051522, 59273370, 350336326, 2076929912, 12328636710, 73241168202, 435453806538, 2590088923960, 15409982499130, 91703551575882, 545793722630878, 3248685323916392

Offset: 1

R. H. Hardin, Feb 05 2012

nonn

Column 1 of A206238.

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

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

Cf. A206238.

Empirical: a(n) = 8*a(n-1) -11*a(n-2) +36*a(n-3) -303*a(n-4) +232*a(n-5) +147*a(n-6) +756*a(n-7) for n>8.

Empirical g.f.: x*(15 - 60*x - 5*x^2 - 720*x^3 + 1585*x^4 + 1366*x^5 + 2793*x^6 - 378*x^7) / ((1 - 4*x)*(1 - x - x^2 - 3*x^3)*(1 - 3*x - 7*x^2 - 63*x^3)). - Colin Barker, Jun 14 2018

A206232 Number of (n+1)X3 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

Original entry on oeis.org

60, 256, 1136, 5728, 31652, 170728, 943584, 5175034, 28475596, 156707492, 861735284, 4742758462, 26087819020, 143545024690, 789722083016, 4344918701514, 23904948840000, 131519096655384, 723594734816028

Offset: 1

R. H. Hardin Feb 05 2012

nonn

Column 2 of A206238

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

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

Empirical: a(n) = 3*a(n-1) +20*a(n-2) -14*a(n-3) -133*a(n-4) +95*a(n-5) +123*a(n-6) +9*a(n-7) -102*a(n-8) for n>10

A206233 Number of (n+1) X 4 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

Original entry on oeis.org

310, 1136, 4456, 27168, 133392, 607008, 3503136, 17206032, 78302496, 451903008, 2219576592, 10101020448, 58295486496, 286325378832, 1303031636256, 7520117756448, 36935973867792, 168091081075488, 970095190580256

Offset: 1

R. H. Hardin, Feb 05 2012

nonn

Column 3 of A206238.

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

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

Cf. A206238.

Empirical: a(n) = a(n-1) + 129*a(n-3) - 129*a(n-4) for n>7.

Empirical g.f.: 2*x*(155 + 413*x + 1660*x^2 - 8639*x^3 - 165*x^4 + 22668*x^5 - 16860*x^6) / ((1 - x)*(1 - 129*x^3)). - Colin Barker, Jun 14 2018

A206234 Number of (n+1) X 5 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1640, 5728, 27168, 283728, 1236432, 9042600, 95322432, 419146392, 3065437344, 32314300392, 142090622832, 1039183255560, 10954547828832, 48168721135992, 352283123630784, 3713591713969992, 16329196465097232, 119423978910831720

Offset: 1

R. H. Hardin, Feb 05 2012

nonn

Column 4 of A206238.

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

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

Cf. A206238.

Empirical: a(n) = a(n-1) + 339*a(n-3) - 339*a(n-4) for n>8.

Empirical g.f.: 8*x*(205 + 511*x + 2680*x^2 - 37425*x^3 - 54141*x^4 + 67251*x^5 - 86751*x^6 + 107163*x^7) / ((1 - x)*(1 - 339*x^3)). - Colin Barker, Jun 14 2018

A206235 Number of (n+1)X6 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

Original entry on oeis.org

8910, 31652, 133392, 1236432, 10915392, 118573968, 1122086640, 10022726928, 109206613488, 1033441784400, 9230931489648, 100579291011408, 951799883421360, 8501687901954768, 92633527021495728, 876607692631061520

Offset: 1

R. H. Hardin Feb 05 2012

nonn

Column 5 of A206238

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

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

Empirical: a(n) = a(n-1) +921*a(n-3) -921*a(n-4) for n>9

A206236 Number of (n+1)X7 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

Original entry on oeis.org

51066, 170728, 607008, 9042600, 118573968, 1448239080, 22535636736, 303011941944, 3712941210144, 57939122017416, 779043702707184, 9545971851249384, 148961482706745696, 2002921359660139224

Offset: 1

R. H. Hardin Feb 05 2012

nonn

Column 6 of A206238

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

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

Empirical: a(n) = a(n-1) +2571*a(n-3) -2571*a(n-4) for n>10

A206237 Number of (n+1) X 8 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

Original entry on oeis.org

294546, 943584, 3503136, 95322432, 1122086640, 22535636736, 649065145152, 8026428934128, 163621204516992, 4735717646406528, 58825697658136176, 1199179807904946432, 34708074630513355776, 431133538136479945968

Offset: 1

R. H. Hardin, Feb 05 2012

nonn

Column 7 of A206238.

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

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

Empirical: a(n) = a(n-1) +7329*a(n-3) -7329*a(n-4) for n>11.

cp's OEIS Frontend

A206230 Number of (n+1)X(n+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

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A206231 Number of (n+1) X 2 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

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A206232 Number of (n+1)X3 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

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A206233 Number of (n+1) X 4 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

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A206234 Number of (n+1) X 5 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

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A206235 Number of (n+1)X6 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

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A206236 Number of (n+1)X7 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

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A206237 Number of (n+1) X 8 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

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