A280069 -id:A280069 - cp's OEIS frontend

A280064 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 5, 15, 39, 104, 281, 771, 2122, 5858, 16174, 44694, 123510, 341403, 943694, 2608709, 7211359, 19935055, 55108220, 152341402, 421132682, 1164181573, 3218268552, 8896600238, 24593808939, 67987267220, 187944382019, 519554527901

Offset: 1

R. H. Hardin, Dec 25 2016

nonn

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

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

Column 3 of A280069.

Empirical: a(n) = 3*a(n-1) + a(n-2) - 6*a(n-3) + 5*a(n-4) - 2*a(n-5) - 2*a(n-6) - a(n-7) for n>9.

Empirical g.f.: x*(1 + x)*(1 - 2*x + 4*x^3 - 8*x^4 + 2*x^5 - x^6 - x^7) / ((1 - x + x^2)*(1 - 2*x - 4*x^2 + 4*x^3 + 3*x^4 + x^5)). - Colin Barker, Feb 12 2019

A280065 Number of nX4 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

2, 4, 15, 52, 170, 603, 2157, 7777, 28195, 102429, 372430, 1355019, 4930977, 17946466, 65320396, 237756751, 865411414, 3150039989, 11465974491, 41735611962, 151915810407, 552967220870, 2012778077066, 7326430841669

Offset: 1

R. H. Hardin, Dec 25 2016

nonn

Column 4 of A280069.

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

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

Cf. A280069.

Empirical: a(n) = 4*a(n-1) +4*a(n-2) -21*a(n-3) -4*a(n-4) +34*a(n-5) +25*a(n-6) -37*a(n-7) -82*a(n-8) +44*a(n-9) +36*a(n-10) +6*a(n-11) -a(n-12) -5*a(n-13) -3*a(n-14) +a(n-15) for n>18

A280066 Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

3, 9, 39, 170, 790, 3729, 17468, 82769, 394904, 1890877, 9080800, 43650638, 210047292, 1011165147, 4869719373, 23456281889, 113000007399, 544411868911, 2623011742357, 12638188505237, 60894518951302, 293410920660702

Offset: 1

R. H. Hardin, Dec 25 2016

nonn

Column 5 of A280069.

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

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

Cf. A280069.

Empirical: a(n) = 8*a(n-1) -4*a(n-2) -97*a(n-3) +176*a(n-4) +339*a(n-5) -1073*a(n-6) -47*a(n-7) +3377*a(n-8) -3342*a(n-9) -7621*a(n-10) +13813*a(n-11) +10465*a(n-12) -31408*a(n-13) -5811*a(n-14) +90585*a(n-15) -69504*a(n-16) -167596*a(n-17) +292370*a(n-18) -85078*a(n-19) -228536*a(n-20) +394124*a(n-21) -113838*a(n-22) -192578*a(n-23) +250274*a(n-24) -199426*a(n-25) -58314*a(n-26) +185492*a(n-27) -136476*a(n-28) +48376*a(n-29) +64368*a(n-30) -69640*a(n-31) +27472*a(n-32) +2400*a(n-33) -15956*a(n-34) +6480*a(n-35) for n>40

A280067 Number of nX6 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

5, 19, 104, 603, 3729, 23564, 145485, 915505, 5786757, 36671797, 233383456, 1487001440, 9487581421, 60571549809, 386914206005, 2472215283933, 15799867880212, 100989585485103, 645564463469368, 4126929495349807

Offset: 1

R. H. Hardin, Dec 25 2016

nonn

Column 6 of A280069.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 87

Cf. A280069.

Empirical recurrence of order 87 (see link above)

A280068 Number of nX7 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

8, 41, 281, 2157, 17468, 145485, 1188839, 9934415, 83159859, 698377561, 5887978374, 49721599049, 420447933252, 3558743911515, 30138816610398, 255354080222866, 2164080579680386, 18343719103540772, 155508281837894034

Offset: 1

R. H. Hardin, Dec 25 2016

nonn

Column 7 of A280069.

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

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

Cf. A280069.

A280063 Number of n X n 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

1, 1, 5, 52, 790, 23564, 1188839, 110266512, 18113056960, 5286615353516, 2755789744812452

Offset: 1

R. H. Hardin, Dec 25 2016

nonn

Diagonal of A280069.

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

Cf. A280069.

cp's OEIS Frontend

A280064 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280065 Number of nX4 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280066 Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280067 Number of nX6 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280068 Number of nX7 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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A280063 Number of n X n 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

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