A268789 -id:A268789 - cp's OEIS frontend

A268782 Number of n X n binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

0, 5, 72, 1714, 67100, 4725018, 611932378, 148013550916, 67580406047498, 58605374440440754, 97015414668307967168, 307604236621005318739500, 1873151902121241161650454526, 21951627197224261891003815976598

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Diagonal of A268789.

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

R. H. Hardin, Table of n, a(n) for n = 1..26

Cf. A268789.

A268783 Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

1, 5, 17, 48, 131, 338, 850, 2091, 5061, 12095, 28608, 67095, 156244, 361652, 832757, 1908885, 4358285, 9915728, 22489147, 50862918, 114743814, 258261695, 580072917, 1300393467, 2910078592, 6501783407, 14504787560, 32313853992, 71896385513

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

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

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

Column 2 of A268789.

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

Empirical g.f.: x*(1 + 3*x + 4*x^2 + x^3) / (1 - x - 2*x^2 - x^3)^2. - Colin Barker, Jan 15 2019

A268784 Number of n X 3 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

2, 17, 72, 302, 1144, 4207, 14984, 52335, 179854, 610504, 2051436, 6836258, 22622554, 74418562, 243553160, 793537401, 2575357784, 8329124488, 26854438804, 86342760711, 276915214344, 886094782671, 2829527431748, 9018299661270

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

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

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

Column 3 of A268789.

Empirical: a(n) = 2*a(n-1) + 9*a(n-2) - 2*a(n-3) - 33*a(n-4) - 42*a(n-5) - 14*a(n-6) + 10*a(n-7) + 8*a(n-8) - a(n-10).

Empirical g.f.: x*(2 + 13*x + 20*x^2 + 9*x^3 - 8*x^4 - 10*x^5 - 4*x^6) / ((1 + x)^2*(1 - 2*x - 3*x^2 - x^3 + x^4)^2). - Colin Barker, Jan 15 2019

A268785 Number of nX4 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

5, 48, 302, 1714, 9085, 46195, 228384, 1105510, 5267662, 24786180, 115455033, 533317129, 2446323573, 11154503019, 50600348892, 228514035985, 1027932765869, 4607917805325, 20591918472965, 91765529043193, 407916504889146

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 4 of A268789.

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

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

Cf. A268789.

Empirical: a(n) = 2*a(n-1) +19*a(n-2) +10*a(n-3) -122*a(n-4) -320*a(n-5) -295*a(n-6) +8*a(n-7) +176*a(n-8) +20*a(n-9) -98*a(n-10) -6*a(n-11) +43*a(n-12) -6*a(n-13) -11*a(n-14) +6*a(n-15) -a(n-16)

A268786 Number of nX5 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

10, 131, 1144, 9085, 67100, 477128, 3295246, 22302699, 148575958, 977609634, 6368239274, 41140907455, 263939673228, 1683296018391, 10680625988516, 67468330344536, 424526386272378, 2661981983940811, 16640406499054332

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 5 of A268789.

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

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

Cf. A268789.

Empirical: a(n) = 2*a(n-1) +41*a(n-2) +54*a(n-3) -509*a(n-4) -2182*a(n-5) -2830*a(n-6) +1766*a(n-7) +7914*a(n-8) +2584*a(n-9) -10583*a(n-10) -6092*a(n-11) +11506*a(n-12) +5348*a(n-13) -11688*a(n-14) -620*a(n-15) +9251*a(n-16) -4462*a(n-17) -3137*a(n-18) +4774*a(n-19) -2365*a(n-20) +338*a(n-21) +198*a(n-22) -106*a(n-23) +12*a(n-24) +4*a(n-25) -a(n-26)

A268787 Number of nX6 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

20, 338, 4207, 46195, 477128, 4725018, 45515227, 429442918, 3988796543, 36591758790, 332327545513, 2993282062865, 26773510121640, 238060527618025, 2105957538309226, 18547209960131466, 162707970808249851

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 6 of A268789.

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

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

Cf. A268789.

Empirical: a(n) = 2*a(n-1) +83*a(n-2) +210*a(n-3) -1918*a(n-4) -13444*a(n-5) -27431*a(n-6) +22868*a(n-7) +172414*a(n-8) +91292*a(n-9) -572846*a(n-10) -576908*a(n-11) +1569339*a(n-12) +1662464*a(n-13) -4129647*a(n-14) -2739590*a(n-15) +10005684*a(n-16) +128072*a(n-17) -18820309*a(n-18) +14239344*a(n-19) +18275195*a(n-20) -39512592*a(n-21) +16595129*a(n-22) +32600294*a(n-23) -63035320*a(n-24) +55225574*a(n-25) -27556538*a(n-26) +5959238*a(n-27) +1367780*a(n-28) -935764*a(n-29) -205936*a(n-30) +253428*a(n-31) -6946*a(n-32) -44268*a(n-33) +5192*a(n-34) +6896*a(n-35) -1085*a(n-36) -848*a(n-37) +74*a(n-38) +94*a(n-39) +3*a(n-40) -6*a(n-41) -a(n-42)

A268788 Number of nX7 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

38, 850, 14984, 228384, 3295246, 45515227, 611932378, 8057509992, 104456486696, 1337467436839, 16954554895936, 213155407369839, 2661273257222436, 33030289066656341, 407868045265169610, 5014148928763408926

Offset: 1

R. H. Hardin, Feb 13 2016

nonn

Column 7 of A268789.

			Some solutions for n=3
..0..0..0..0..0..1..0. .0..1..0..0..1..0..0. .1..1..0..0..0..1..0
..1..0..0..0..0..0..1. .0..0..0..1..0..0..0. .0..0..0..0..0..0..0
..0..0..0..1..0..0..1. .0..1..0..0..0..1..0. .1..0..0..0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 68

Cf. A268789.

Empirical recurrence of order 68 (see link above)

cp's OEIS Frontend

A268782 Number of n X n binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268783 Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268784 Number of n X 3 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268785 Number of nX4 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268786 Number of nX5 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268787 Number of nX6 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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A268788 Number of nX7 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

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