A208688 -id:A208688 - cp's OEIS frontend

A208689 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

6, 36, 78, 282, 768, 2430, 7086, 21588, 64230, 193554, 579264, 1740054, 5216502, 15655428, 46956702, 140885610, 422631744, 1267935822, 3803741790, 11411331636, 34233822966, 102701747106, 308104791168, 924315101862, 2772944127078

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 3 of A208688.

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

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

Cf. A208688.

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 3*a(n-3).
Conjectures from Colin Barker, Mar 07 2018: (Start)
G.f.: 6*x*(1 + 4*x - 3*x^2) / ((1 - 3*x)*(1 + x - x^2)).
a(n) = 2^(-n)*(5*6^(2+n) + (75-27*sqrt(5))*(-1+sqrt(5))^n + 3*(-1-sqrt(5))^n*(25+9*sqrt(5))) / 55.
(End)

A208683 Number of n X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 16, 78, 927, 12096, 301035, 6398617, 358035204, 14996975204, 1866358422700, 142488171799491, 43994512655386488, 5996882020078059149, 4716359423241404452425, 1123534623785504112746542

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Diagonal of A208688.

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

R. H. Hardin, Table of n, a(n) for n = 1..37

Cf. A208688.

A208684 Number of nX4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

10, 100, 282, 927, 3430, 11067, 34627, 111642, 356116, 1121500, 3542847, 11196360, 35283685, 111150345, 350234962, 1103073000, 3473204686, 10936009567, 34431544350, 108396961047, 341246282767, 1074267088938, 3381794658280

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Column 4 of A208688

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

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

Empirical: a(n) = 4*a(n-1) -3*a(n-2) +10*a(n-3) -27*a(n-4) -6*a(n-5) -15*a(n-6) +51*a(n-7) +41*a(n-8) +31*a(n-9) -51*a(n-10) -29*a(n-11) -27*a(n-12) +15*a(n-13) +6*a(n-14) +3*a(n-15) -4*a(n-16) +a(n-17) +a(n-19)

A208685 Number of nX5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

16, 256, 768, 2889, 12096, 41013, 133207, 444912, 1448128, 4616800, 14733663, 46884096, 148366461, 468807885, 1480447408, 4669224000, 14715790096, 46366826149, 146050380000, 459933577353, 1448231824455, 4559797881648

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Column 5 of A208688

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

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

Empirical: a(n) = 4*a(n-1) -3*a(n-2) +10*a(n-3) -27*a(n-4) -6*a(n-5) -15*a(n-6) +51*a(n-7) +41*a(n-8) +31*a(n-9) -51*a(n-10) -29*a(n-11) -27*a(n-12) +15*a(n-13) +6*a(n-14) +3*a(n-15) -4*a(n-16) +a(n-17) +a(n-19)

A208686 Number of nX6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

26, 676, 2430, 11727, 66094, 301035, 1332721, 6219706, 28669412, 130450900, 599156271, 2760581304, 12692272021, 58421183145, 269289045586, 1241270953000, 5722274656706, 26389387599127, 121715139738150, 561405501868311

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Column 6 of A208688

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

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

Empirical: a(n) = 6*a(n-1) -7*a(n-2) +31*a(n-3) -128*a(n-4) -30*a(n-5) -116*a(n-6) +788*a(n-7) +798*a(n-8) +678*a(n-9) -2778*a(n-10) -1872*a(n-11) -1842*a(n-12) +3336*a(n-13) +1554*a(n-14) +378*a(n-15) -2736*a(n-16) +912*a(n-17) +312*a(n-18) +1590*a(n-19) -540*a(n-20) -228*a(n-21) -222*a(n-22) +210*a(n-23) -86*a(n-24) +24*a(n-25) -38*a(n-26) +8*a(n-27) -a(n-28) -a(n-30) +a(n-31)

A208687 Number of nX7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

42, 1764, 7086, 40581, 269766, 1346961, 6398617, 31733422, 152209092, 711191700, 3333256899, 15574230936, 72263776797, 334784881455, 1550207903794, 7167239737000, 33109416636066, 152910959100921, 705957016908150

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Column 7 of A208688

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

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

Empirical: a(n) = 6*a(n-1) -7*a(n-2) +31*a(n-3) -128*a(n-4) -30*a(n-5) -116*a(n-6) +788*a(n-7) +798*a(n-8) +678*a(n-9) -2778*a(n-10) -1872*a(n-11) -1842*a(n-12) +3336*a(n-13) +1554*a(n-14) +378*a(n-15) -2736*a(n-16) +912*a(n-17) +312*a(n-18) +1590*a(n-19) -540*a(n-20) -228*a(n-21) -222*a(n-22) +210*a(n-23) -86*a(n-24) +24*a(n-25) -38*a(n-26) +8*a(n-27) -a(n-28) -a(n-30) +a(n-31)

A208690 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

9, 81, 189, 927, 2889, 11727, 40581, 154359, 554733, 2062215, 7512453, 27700479, 101402109, 372809655, 1367107173, 5021003151, 18423673101, 67639822407, 248247487989, 911283026751, 3344800820445, 12277727839863, 45065827217925

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 4 of A208688.

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

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

Cf. A208688.

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

Empirical g.f.: 9*x*(1 + 8*x + 2*x^2 - 10*x^3) / (1 - x - 10*x^2 - 2*x^3 + 10*x^4). - Colin Barker, Jul 05 2018

A208691 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

14, 196, 490, 3430, 12096, 66094, 269766, 1331988, 5795314, 27403166, 122618944, 569030406, 2577715070, 11864806436, 54038278042, 247841874742, 1131464944960, 5181256121790, 23678302787734, 108354576646260, 495403870286178

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 5 of A208688.

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

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

Cf. A208688.

Empirical: a(n) = a(n-1) + 17*a(n-2) + 4*a(n-3) - 32*a(n-4).

Empirical g.f.: 14*x*(1 + 13*x + 4*x^2 - 32*x^3) / (1 - x - 17*x^2 - 4*x^3 + 32*x^4). - Colin Barker, Jul 05 2018

A208692 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

21, 441, 1113, 11067, 41013, 301035, 1346961, 8556723, 42184905, 249260739, 1292345649, 7358809899, 39164938617, 218805732243, 1180444035057, 6530395532955, 35479909625769, 195286010577987, 1064871399311265

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 6 of A208688.

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

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

Cf. A208688.

Empirical: a(n) = a(n-1) + 26*a(n-2) + 6*a(n-3) - 78*a(n-4).

Empirical g.f.: 21*x*(1 + 20*x + 6*x^2 - 78*x^3) / (1 - x - 26*x^2 - 6*x^3 + 78*x^4). - Colin Barker, Jul 05 2018

A208693 Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

31, 961, 2449, 34627, 133207, 1332721, 6398617, 53340739, 290904031, 2188890625, 12862463425, 91246001059, 560219364679, 3840575264305, 24195101079817, 162595230479203, 1039929864328591, 6907596215160961, 44573099803921777

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 7 of A208688.

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

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

Cf. A208688.

Empirical: a(n) = a(n-1) + 39*a(n-2) + 9*a(n-3) - 180*a(n-4).

Empirical g.f.: 31*x*(1 + 30*x + 9*x^2 - 180*x^3) / ((1 + 5*x)*(1 - 6*x - 9*x^2 + 36*x^3)). - Colin Barker, Jul 05 2018

cp's OEIS Frontend

A208689 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208683 Number of n X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A208684 Number of nX4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208685 Number of nX5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208686 Number of nX6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208687 Number of nX7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208690 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208691 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208692 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208693 Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Views

Author