A186482 -id:A186482 - cp's OEIS frontend

A186474 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

256, 205, 1098, 1251, 4895, 5955, 20079, 27101, 84228, 123227, 354915, 553287, 1501107, 2465976, 6374253, 10928793, 27157017, 48218637, 116026140, 211997451, 496891083, 929460999, 2132220387, 4065922560, 9164874045, 17754363633

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 1 of A186482.

			Some solutions for 3 X 2:
..0..0....2..2....3..3....3..3....2..0....2..2....2..3....0..2....2..0....0..0
..3..0....0..0....1..0....3..3....0..2....1..0....3..0....3..0....0..2....1..0
..0..3....0..0....0..1....3..3....1..2....0..1....0..3....0..3....0..0....1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A186482.

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-4) - 3*a(n-5) for n>12.

Empirical g.f.: x*(256 - 307*x + 176*x^2 + 181*x^3 - 109*x^4 - 211*x^5 - 88*x^6 + 191*x^7 - 19*x^8 - 2*x^9 + 2*x^10 + 2*x^11) / ((1 - x)*(1 - x - 3*x^2 + 3*x^3 - 3*x^4)). - Colin Barker, Feb 28 2018

A186473 Number of (n+1)X(n+1) 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

256, 362, 4686, 16762, 107353, 305089, 1849873, 5977657, 34498177, 116855689, 634602529, 2242113937, 11691520969, 42863613697, 216155958361, 816595120705, 4006518195025, 15513728255737, 74427875789953, 294085455103369

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Diagonal of A186482

			Some solutions for 3X3
..2..0..3....1..0..1....1..2..1....3..2..0....2..0..0....0..0..0....2..0..0
..0..2..0....0..1..0....2..1..2....0..0..2....0..2..0....0..0..0....0..0..0
..0..0..2....0..0..1....1..2..1....0..0..3....3..0..2....1..1..1....0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..29

A186475 Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

Original entry on oeis.org

205, 362, 701, 2049, 3442, 8223, 14492, 35081, 64280, 150785, 281928, 646756, 1233097, 2780008, 5384887, 11965960, 23479960, 51563275, 102260008, 222407905, 444938056, 960071644, 1934442193, 4147066744, 8404992631, 17923081288

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 2 of A186482.

			Some solutions for 5 X 3:
..2..0..2....2..1..0....0..0..3....1..2..0....3..1..0....0..2..1....0..3..0
..0..2..0....2..0..1....0..0..0....1..0..2....0..0..1....0..0..2....2..0..3
..1..0..2....0..2..0....0..0..0....0..1..0....0..0..0....0..0..0....0..2..0
..0..1..0....3..0..2....2..0..0....0..0..1....3..0..0....3..0..0....0..0..2
..0..0..1....0..3..0....0..2..2....0..0..1....2..3..0....0..3..1....0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A186482.

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-4) - 3*a(n-5) for n>13.

Empirical g.f.: x*(205 - 48*x - 433*x^2 + 1153*x^3 - 1116*x^4 - 110*x^5 + 336*x^6 + 112*x^7- 33*x^8 + 3*x^9 + x^10 + 2*x^12) / ((1 - x)*(1 - x - 3*x^2 + 3*x^3 - 3*x^4)). - Colin Barker, Apr 18 2018

A186476 Number of (n+1)X4 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

1098, 701, 4686, 4810, 20224, 21760, 82632, 101108, 344804, 465884, 1445243, 2112183, 6085048, 9483898, 25738600, 42272077, 109291705, 187344208, 465619270, 826593388, 1989294067, 3634249423, 8519209648, 15933856258, 36556619512

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 3 of A186482

			Some solutions for 3X4
..2..0..1..0....2..2..2..0....0..0..1..1....0..3..0..2....0..1..0..3
..0..2..0..1....0..0..0..2....0..0..0..1....2..0..3..0....0..0..1..0
..2..0..2..2....0..0..0..2....1..0..0..0....0..2..0..3....0..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-4)-3*a(n-5) for n>14

A186477 Number of (n+1)X5 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

1251, 2049, 4810, 16762, 25633, 67714, 101305, 286290, 456113, 1219034, 2037173, 5189546, 9017049, 22136029, 39734818, 94665157, 174517432, 405721297, 764487337, 1742099164, 3341954341, 7491958474, 14584990777, 32261305429

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 4 of A186482

			Some solutions for 3X5
..0..0..0..3..0....0..0..0..1..0....2..0..0..0..0....2..1..0..0..0
..2..0..0..0..3....3..0..0..0..1....2..0..0..0..0....3..0..1..0..0
..0..2..0..0..2....2..3..0..0..0....2..0..0..0..1....0..3..0..1..3

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-4)-3*a(n-5) for n>15

A186478 Number of (n+1)X6 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

4895, 3442, 20224, 25633, 107353, 108025, 433513, 479785, 1793817, 2226665, 7478693, 10225073, 31371137, 46298817, 132181633, 207648469, 559418905, 924724441, 2376589225, 4095459817, 10129319461, 18060113137, 43291468321

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 5 of A186482

			Some solutions for 3X6
..1..0..0..0..2..1....0..1..0..1..0..1....0..0..0..0..3..0....2..0..1..0..0..0
..1..0..0..0..0..2....3..0..1..0..1..1....0..0..0..0..0..3....0..2..0..1..0..0
..0..1..0..0..0..0....0..3..0..1..1..2....0..0..0..0..0..0....3..0..2..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-4)-3*a(n-5) for n>16

A186479 Number of (n+1)X7 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

5955, 8223, 21760, 67714, 108025, 305089, 418177, 1286113, 1812049, 5368065, 8100785, 22640045, 36286649, 96020681, 161275017, 408409609, 713044957, 1742523169, 3140266657, 7453942513, 13786320241, 31954929709, 60372875257

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 6 of A186482

			Some solutions for 3X7
..2..0..0..0..2..0..0....3..1..0..2..0..1..0....1..1..0..2..0..2..0
..3..0..0..0..0..2..0....2..0..1..0..2..0..1....1..0..1..0..2..0..2
..0..3..0..0..0..0..2....0..2..0..1..0..2..0....0..1..0..1..0..2..3

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-4)-3*a(n-5) for n>17

A186480 Number of (n+1)X8 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

20079, 14492, 82632, 101305, 433513, 418177, 1849873, 1894849, 7687009, 8602033, 31645329, 39574001, 131802797, 181420169, 553069145, 820669641, 2331052105, 3678141757, 9868524241, 16371829777, 41936161201, 72480530737, 178779125389

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 7 of A186482

			Some solutions for 3X8
..0..0..0..0..1..0..0..0....2..0..1..0..1..0..2..0....1..0..2..0..0..0..3..3
..3..0..0..0..0..1..0..0....0..2..0..1..0..1..0..2....0..1..0..2..0..0..0..3
..2..3..0..0..0..0..1..0....3..0..2..0..1..0..1..0....3..0..1..0..2..0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-4)-3*a(n-5) for n>18

A186481 Number of (n+1)X9 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

27101, 35081, 101108, 286290, 479785, 1286113, 1894849, 5977657, 8078233, 25049545, 34600393, 103930809, 154520201, 437740901, 693356465, 1854858401, 3085313121, 7883094433, 13654582357, 33612555865, 60183013369, 143706271561

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 8 of A186482

			Some solutions for 3X9
..1..0..3..0..1..0..1..0..1....2..2..0..2..0..1..0..0..0
..0..1..0..3..0..1..0..1..0....2..0..2..0..2..0..1..0..0
..2..0..1..0..3..0..1..0..1....0..2..0..2..0..2..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-4)-3*a(n-5) for n>19

cp's OEIS Frontend

A186474 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

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A186473 Number of (n+1)X(n+1) 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

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A186475 Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

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A186476 Number of (n+1)X4 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

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A186477 Number of (n+1)X5 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

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A186478 Number of (n+1)X6 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

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A186479 Number of (n+1)X7 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

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A186480 Number of (n+1)X8 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

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A186481 Number of (n+1)X9 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

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