A186472 -id:A186472 - cp's OEIS frontend

A186464 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

81, 83, 277, 367, 966, 1321, 3078, 4553, 10028, 15650, 32786, 53166, 107524, 179614, 353932, 604474, 1168188, 2028530, 3863852, 6793514, 12800564, 22716978, 42458812, 75878698, 140963524, 253237282, 468324588, 844629530, 1556731220

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 1 of A186472.

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

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

Cf. A186472.

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 4*a(n-4) - 2*a(n-5) for n>10.

Empirical g.f.: x*(81 - 79*x + 30*x^2 + 54*x^3 - 37*x^4 - 40*x^5 - 4*x^6 + 26*x^7 - 2*x^8 + x^9) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Feb 28 2018

A186463 Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

81, 129, 942, 3186, 13278, 34314, 136086, 399018, 1537038, 4607034, 16888062, 51777498, 185254926, 580089834, 2037893214, 6478793466, 22450788942, 72203998026, 247694103486, 803564559834, 2735884703406, 8933648141802

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Diagonal of A186472

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

R. H. Hardin, Table of n, a(n) for n = 1..23

A186465 Number of (n+1) X 3 0..2 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

83, 129, 243, 562, 903, 1754, 2937, 5790, 9993, 19236, 33546, 63642, 112278, 210972, 375366, 700068, 1253442, 2324820, 4182330, 7725252, 13947186, 25682700, 46491258, 85412820, 154924338, 284132892, 516138474, 945381252, 1719241122

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 2 of A186472.

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

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

Cf. A186472.

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 4*a(n-4) - 2*a(n-5) for n>11.

Empirical g.f.: x*(83 - 37*x - 98*x^2 + 279*x^3 - 280*x^4 + 8*x^5 + 60*x^6 + 12*x^7 + 4*x^8 - 2*x^9 + x^10) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Apr 18 2018

A186466 Number of (n+1) X 4 0..2 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

277, 243, 942, 1203, 3190, 4023, 9982, 13985, 32390, 48553, 105436, 165842, 344498, 562526, 1130820, 1898670, 3724364, 6385226, 12298364, 21417538, 40692652, 71701562, 134848628, 239701634, 447381180, 800490426, 1485546884, 2671168754

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 3 of A186472.

			Some solutions for 3 X 4:
..1..0..1..0....0..0..0..0....1..2..0..1....0..0..0..0....1..0..0..0
..0..1..0..1....1..0..0..0....2..0..2..0....0..0..0..0....0..1..0..0
..2..0..1..2....0..1..0..0....0..2..0..2....1..0..0..2....1..0..1..1

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

Cf. A186472.

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

Empirical g.f.: x*(277 - 311*x + 179*x^2 + 184*x^3 - 294*x^4 - 210*x^5 + 276*x^6 - 170*x^7 + 176*x^8 + 4*x^9 - 2*x^10 + x^11) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Apr 18 2018

A186467 Number of (n+1) X 5 0..2 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

367, 562, 1203, 3186, 4875, 9834, 14883, 31866, 51057, 105398, 174289, 347428, 588058, 1145866, 1976438, 3787644, 6625638, 12540516, 22170114, 41575892, 74087098, 137980420, 247343794, 458282956, 825184634, 1523024532, 2751516210

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 4 of A186472.

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

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

Cf. A186472.

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

Empirical g.f.: x*(367 - 172*x - 288*x^2 + 1686*x^3 - 1920*x^4 + 196*x^5 - 604*x^6 + 1428*x^7 - 1350*x^8 + 1364*x^9 + 36*x^10 - 18*x^11 + 9*x^12) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Apr 18 2018

A186468 Number of (n+1)X6 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

966, 903, 3190, 4875, 13278, 16083, 40626, 52755, 129102, 182841, 418022, 632281, 1362100, 2157562, 4454506, 7311254, 14630604, 24660486, 48209460, 82892994, 159253412, 277942714, 527083732, 930249586, 1747039708, 3109258106

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 5 of A186472

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

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

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

A186469 Number of (n+1) X 7 0..2 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

1321, 1754, 4023, 9834, 16083, 34314, 49407, 109950, 159879, 350418, 540777, 1143302, 1845649, 3753244, 6241282, 12344866, 21014030, 40729476, 70552158, 134674572, 236349786, 446055356, 790511890, 1479273964, 2640888394

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 6 of A186472.

			Some solutions for 3 X 7
..2..0..0..0..2..0..1....2..2..0..0..0..0..1....2..1..0..0..0..1..0
..2..0..0..0..0..2..0....1..0..2..0..0..0..1....1..0..1..0..0..0..1
..2..0..0..0..0..0..2....0..1..0..2..0..0..1....0..1..0..1..0..0..2

R. H. Hardin, Table of n, a(n) for n = 1..170

Cf. A186472.

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

A186470 Number of (n+1)X8 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

3078, 2937, 9982, 14883, 40626, 49407, 136086, 170811, 431658, 564459, 1356918, 1931673, 4382606, 6664633, 14283484, 22714258, 46720546, 76914734, 153497652, 259317918, 505928220, 871401594, 1671620876, 2921206834, 5533505212

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 7 of A186472

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

R. H. Hardin, Table of n, a(n) for n = 1..82

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

A186471 Number of (n+1)X9 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

4553, 5790, 13985, 31866, 52755, 109950, 170811, 399018, 570183, 1266414, 1812423, 3993474, 6107001, 13004678, 20863681, 42650908, 70588930, 140178754, 237788174, 462275652, 798678366, 1528016844, 2676404634, 5059638908, 8953777234

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Column 8 of A186472

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

R. H. Hardin, Table of n, a(n) for n = 1..78

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

cp's OEIS Frontend

A186464 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A186463 Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

A186465 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A186466 Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A186467 Number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A186468 Number of (n+1)X6 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A186469 Number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A186470 Number of (n+1)X8 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A186471 Number of (n+1)X9 0..2 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula