A186462 -id:A186462 - cp's OEIS frontend

A186454 Number of (n+1) X 2 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

16, 21, 42, 61, 106, 151, 245, 359, 567, 840, 1301, 1941, 2977, 4465, 6810, 10247, 15577, 23487, 35635, 53800, 81533, 123193, 186569, 282037, 426954, 645623, 977117, 1477831, 2236287, 3382632, 5118213, 7742397, 11714273, 17721097, 26811194

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 1 of A186462.

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

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

Cf. A186462.

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>8.

Empirical g.f.: x*(16 - 11*x + 9*x^3 - 6*x^4 - 3*x^5 + 2*x^6 + x^7) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Feb 28 2018

A186453 Number of (n+1)X(n+1) binary arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Original entry on oeis.org

16, 30, 111, 309, 797, 1693, 4121, 9477, 22933, 52197, 122109, 277217, 642629, 1463845, 3375245, 7698781, 17693113, 40404005, 92697797, 211861205, 485587357, 1110399969, 2543583205, 5818446165, 13323806077, 30484799837, 69794079385

Offset: 1

R. H. Hardin Feb 22 2011

nonn

Diagonal of A186462

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

R. H. Hardin, Table of n, a(n) for n = 1..39

A186455 Number of (n+1) X 3 binary 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

21, 30, 51, 88, 128, 197, 292, 457, 688, 1058, 1589, 2424, 3651, 5552, 8376, 12709, 19192, 29085, 43952, 66562, 100629, 152332, 230359, 348632, 527296, 797909, 1206940, 1826193, 2762528, 4179698, 6322981, 9566352, 14472171, 21895248

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 2 of A186462.

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

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

Cf. A186462.

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>8.

Empirical g.f.: x*(21 - 12*x - 9*x^2 + 28*x^3 - 30*x^4 + 4*x^5 + 2*x^6 + 4*x^7) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

A186456 Number of (n+1) X 4 binary 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

42, 51, 111, 162, 270, 362, 590, 846, 1362, 1998, 3122, 4622, 7126, 10642, 16286, 24442, 37230, 56046, 85138, 128414, 194754, 294094, 445590, 673362, 1019630, 1541514, 2333390, 3528654, 5340178, 8076974, 12221906, 18487374, 27972502

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 3 of A186462.

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

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

Cf. A186462.

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>9.

Empirical g.f.: x*(42 - 33*x + 9*x^2 + 24*x^3 - 36*x^4 - 16*x^5 + 19*x^6 - 7*x^7 + 16*x^8) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

A186457 Number of (n+1) X 5 binary 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

61, 88, 162, 309, 449, 673, 945, 1493, 2201, 3473, 5177, 7993, 11949, 18289, 27473, 41857, 63041, 95765, 144473, 219105, 330905, 501353, 757677, 1147281, 1734561, 2625569, 3970577, 6008917, 9088537, 13752497, 20802745, 31475673, 47614509

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 4 of A186462.

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

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

Cf. A186462.

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

Empirical g.f.: x*(61 - 34*x - 14*x^2 + 107*x^3 - 115*x^4 - 16*x^5 - 19*x^6 + 45*x^7 - 28*x^8 + 64*x^9) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

A186458 Number of (n+1) X 6 binary 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

106, 128, 270, 449, 797, 1061, 1681, 2285, 3681, 5281, 8437, 12401, 19317, 28641, 44073, 65877, 100705, 151229, 230209, 346689, 526453, 794241, 1204293, 1818849, 2755433, 4164309, 6305265, 9533069, 14429537, 21821729, 33023541, 49948881

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 5 of A186462.

			Some solutions for 3 X 6:
..1..1..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..0....0..0..1..0..1..0
..0..0..1..0..0..0....0..0..0..0..0..1....1..0..0..0..0..0....0..0..0..1..0..1
..0..0..0..1..1..1....0..0..0..0..0..0....1..1..0..0..0..1....0..0..0..0..1..0

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

Cf. A186462.

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

Empirical g.f.: x*(106 - 84*x + 14*x^2 + 121*x^3 - 57*x^4 - 143*x^5 + 45*x^6 - 111*x^7 + 88*x^8 - 44*x^9 + 144*x^10) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

A186459 Number of (n+1) X 7 binary 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

151, 197, 362, 673, 1061, 1693, 2377, 3677, 5073, 7977, 11533, 18221, 26957, 41729, 62105, 95205, 142645, 217581, 327233, 497481, 749885, 1137821, 1717565, 2603089, 3932825, 5956277, 9003685, 13630333, 20610673, 31193705, 47177837, 71391309

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 6 of A186462.

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

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

Cf. A186462.

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

Empirical g.f.: x*(151 - 105*x - 32*x^2 + 251*x^3 - 193*x^4 + 52*x^5 - 190*x^6 + 61*x^7 - 344*x^8 + 260*x^9 - 128*x^10 + 324*x^11) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

A186460 Number of (n+1) X 8 binary 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

245, 292, 590, 945, 1681, 2377, 4121, 5633, 8893, 11977, 19037, 27133, 43249, 63485, 98801, 146333, 225061, 336241, 513933, 771609, 1174525, 1768605, 2685617, 4051469, 6143169, 9277789, 14055269, 21241521, 32162333, 48626537, 73602781

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 7 of A186462.

			Some solutions for 3 X 8:
..0..1..0..0..0..0..0..1....1..0..0..0..1..0..1..0....1..0..0..0..0..0..0..0
..1..0..1..0..0..0..0..0....1..0..0..0..0..1..0..1....1..0..0..0..0..0..0..0
..0..1..0..1..0..0..0..0....1..0..0..0..0..0..1..0....1..0..0..0..0..0..0..0

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

Cf. A186462.

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

Empirical g.f.: x*(245 - 198*x + 6*x^2 + 255*x^3 - 115*x^4 - 144*x^5 + 369*x^6 - 547*x^7 - 36*x^8 - 640*x^9 + 484*x^10 - 300*x^11 + 784*x^12) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 18 2018

A186461 Number of (n+1) X 9 binary 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

359, 457, 846, 1493, 2285, 3677, 5633, 9477, 13245, 20281, 27573, 43177, 62025, 98157, 144825, 224381, 333321, 511281, 765293, 1167881, 1755461, 2669577, 4022697, 6104941, 9213769, 13965837, 21097609, 31954865, 48300653, 73123993

Offset: 1

R. H. Hardin, Feb 22 2011

nonn

Column 8 of A186462.

			Some solutions for 3 X 9:
..0..1..0..1..0..0..0..0..0....1..0..0..1..0..0..0..0..0
..0..0..1..0..1..0..0..0..0....0..0..0..0..1..0..0..0..0
..0..0..0..1..0..1..1..1..1....0..0..0..0..0..1..0..0..1

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

Cf. A186462.

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

Empirical g.f.: x*(359 - 261*x - 68*x^2 + 519*x^3 - 505*x^4 + 244*x^5 + 30*x^6 + 641*x^7 - 1432*x^8 - 12*x^9 - 1624*x^10 + 1200*x^11 - 780*x^12 + 1936*x^13) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 18 2018

cp's OEIS Frontend

A186454 Number of (n+1) X 2 binary 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

A186453 Number of (n+1)X(n+1) binary arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

Views

Author

Keywords

Comments

Examples

Links

A186455 Number of (n+1) X 3 binary 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

A186456 Number of (n+1) X 4 binary 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

A186457 Number of (n+1) X 5 binary 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

A186458 Number of (n+1) X 6 binary 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

A186459 Number of (n+1) X 7 binary 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

A186460 Number of (n+1) X 8 binary 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

A186461 Number of (n+1) X 9 binary 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