A189161 -id:A189161 - cp's OEIS frontend

A189155 Number of nX3 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

8, 64, 512, 3375, 21952, 140608, 884736, 5545233, 34645976, 216000000, 1345572864, 8377795791, 52145952256, 324525966848, 2019487744000, 12566456507249, 78194107594728, 486552055503808, 3027480871826944, 18837870152811039

Offset: 1

R. H. Hardin Apr 17 2011

nonn

Column 3 of A189161

			Some solutions for 4X3
..0..0..1....1..0..1....0..0..0....0..1..1....1..1..0....1..0..0....0..0..1
..0..0..0....0..1..0....0..0..0....1..0..1....0..1..0....0..1..1....1..0..0
..0..1..0....0..0..1....0..0..0....0..0..0....1..0..0....1..1..0....0..0..1
..0..0..0....1..0..0....0..1..1....0..1..0....1..1..0....0..1..1....0..0..0

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

A008937(n+1)^3

Empirical: a(n) = 7*a(n-1) -a(n-2) +a(n-3) -164*a(n-4) +28*a(n-5) +68*a(n-6) +684*a(n-7) +66*a(n-8) +66*a(n-9) -726*a(n-10) -138*a(n-11) -132*a(n-12) +220*a(n-13) +20*a(n-14) +28*a(n-15) -25*a(n-16) -a(n-17) -a(n-18) +a(n-19)

A189154 Number of n X 2 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Original entry on oeis.org

4, 16, 64, 225, 784, 2704, 9216, 31329, 106276, 360000, 1218816, 4124961, 13957696, 47224384, 159769600, 540516001, 1828588644, 6186137104, 20927672896, 70798034241, 239508444816, 810252019600, 2741064339456, 9272956793409

Offset: 1

R. H. Hardin, Apr 17 2011

nonn

Column 2 of A189161.

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

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

Cf. A008937, A189161.

a(n) = A008937(n+1)^2.
Empirical: a(n) = 4*a(n-1) - a(n-2) - 14*a(n-4) + 4*a(n-5) + 2*a(n-6) + 8*a(n-7) - a(n-8) - a(n-10).
Empirical g.f.: x*(4 + 4*x^2 - 15*x^3 + 4*x^4 + x^5 + 8*x^6 - x^7 - x^9) / ((1 - x)*(1 + x + x^2 - x^3)*(1 - x - x^2 - x^3)*(1 - 3*x - x^2 - x^3)). - Colin Barker, Feb 28 2018

A189156 Number of nX4 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Original entry on oeis.org

15, 225, 3375, 37976, 424401, 4597967, 48460966, 507947896, 5289780940, 54890361712, 568739622865, 5886254888757, 60885233141712, 629580674428109, 6508873299252199, 67284551942503294, 695503798053171610

Offset: 1

R. H. Hardin Apr 17 2011

nonn

Column 4 of A189161

			Some solutions for 5X4
..0..0..0..1....0..0..0..1....0..0..1..0....0..0..0..1....0..0..0..1
..1..1..1..0....1..1..0..0....1..1..0..1....1..1..0..1....1..1..0..1
..0..0..0..1....1..0..1..1....1..1..1..0....0..1..0..1....0..1..1..0
..0..0..0..0....0..0..0..1....0..1..0..1....1..1..1..1....1..1..0..1
..1..1..1..1....0..1..1..0....0..1..1..0....0..1..0..0....0..1..0..0

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

A189157 Number of n X 5 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Original entry on oeis.org

28, 784, 21952, 424401, 8210464, 151889331, 2710884810, 48083827685, 844714479714, 14772128520081, 257802672361640, 4491710608316816, 78198928468727304, 1360792591701114315, 23673324742422186018

Offset: 1

R. H. Hardin, Apr 17 2011

nonn

Column 5 of A189161.

			Some solutions for 4 X 5
..0..1..0..1..0....0..0..1..0..1....0..1..0..0..1....0..0..0..0..1
..0..0..1..0..0....1..0..1..0..1....1..1..1..1..1....1..1..1..0..0
..0..1..0..0..1....0..0..1..0..1....0..1..1..0..1....0..1..0..1..1
..1..1..1..0..0....0..1..0..0..0....0..1..1..0..0....1..1..0..0..1

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

Cf. A189161.

A189158 Number of nX6 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Original entry on oeis.org

52, 2704, 140608, 4597967, 151889331, 4708773306, 139543984265, 4101554902927, 118889716429242, 3425594682105277, 98397912139545475, 2819403207915017394, 80693441112166000473, 2307804705252673221664, 65972623009915917276895

Offset: 1

R. H. Hardin Apr 17 2011

nonn

Column 6 of A189161

			Some solutions for 4X6
..0..1..1..1..1..1....0..0..1..0..0..0....0..0..0..1..0..1....0..1..1..1..1..1
..0..0..0..1..0..0....0..1..0..0..0..1....0..0..1..0..0..0....0..0..0..0..1..0
..0..1..0..1..1..1....0..1..0..0..1..0....0..0..0..0..0..1....0..0..0..1..0..0
..0..0..1..0..1..0....0..1..1..0..0..0....0..1..1..1..0..0....0..1..0..1..0..0

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

A189159 Number of nX7 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Original entry on oeis.org

96, 9216, 884736, 48460966, 2710884810, 139543984265, 6787471566616, 327166323321331, 15463232072168424, 725494470365730502, 33890063050246876236, 1577540791665774040985, 73320840584238660162738

Offset: 1

R. H. Hardin Apr 17 2011

nonn

Column 7 of A189161

			Some solutions for 4X7
..0..0..0..0..0..0..1....0..0..1..0..1..1..1....0..0..1..0..0..0..1
..0..0..0..1..0..0..0....0..0..1..0..1..0..0....0..0..1..0..1..0..0
..0..0..0..0..1..0..0....0..0..0..0..1..0..1....0..0..0..0..1..0..1
..0..0..0..1..0..0..0....0..1..1..0..1..0..0....0..0..1..0..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..145

A189160 Number of nX8 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Original entry on oeis.org

177, 31329, 5545233, 507947896, 48083827685, 4101554902927, 327166323321331, 25828698626846656, 1988132110003598299, 151712463019974271421, 11512137558937549516129, 869513813648725138555115

Offset: 1

R. H. Hardin Apr 17 2011

nonn

Column 8 of A189161

			Some solutions for 4X8
..0..0..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..0..0..0..1....0..0..0..0..0..1..0..0....0..0..1..0..1..0..0..0
..0..0..0..0..1..0..0..0....0..0..0..1..0..1..0..1....0..0..0..0..0..0..0..0
..0..0..0..0..0..1..0..0....0..0..0..0..0..1..0..0....0..0..0..1..0..0..0..0

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

A189152 Number of n X n binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Original entry on oeis.org

2, 16, 512, 37976, 8210464, 4708773306, 6787471566616, 25828698626846656, 247502169348575094540, 6064620415913633106142608

Offset: 1

R. H. Hardin Apr 17 2011

nonn

Diagonal of A189161

			Some solutions for 4X4
..0..0..0..0....0..1..0..1....0..1..1..0....0..1..1..1....1..1..1..0
..0..0..0..0....1..0..0..1....1..1..0..0....0..1..0..1....1..1..0..0
..0..1..0..1....1..0..0..1....0..0..0..1....1..1..1..0....0..1..1..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..1....0..0..1..0

cp's OEIS Frontend

A189155 Number of nX3 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A189154 Number of n X 2 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A189156 Number of nX4 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Views

Author

Keywords

Comments

Examples

Links

A189157 Number of n X 5 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A189158 Number of nX6 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Views

Author

Keywords

Comments

Examples

Links

A189159 Number of nX7 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Views

Author

Keywords

Comments

Examples

Links

A189160 Number of nX8 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Views

Author

Keywords

Comments

Examples

Links

A189152 Number of n X n binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

Views

Author

Keywords

Comments

Examples