A231227 -id:A231227 - cp's OEIS frontend

A231221 Number of (n+2) X (2+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

2, 4, 8, 17, 45, 103, 264, 676, 1724, 4501, 11679, 30579, 80180, 210494, 553858, 1457853, 3840945, 10124071, 26693522, 70402100, 185706800, 489925347, 1292616577, 3410640207, 8999588762, 23747752874, 62666069376, 165367179091

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

			Some solutions for n=5:
..0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0....0..0..0..0
..0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0....0..0..0..0
..1..1..0..0....0..0..1..1....0..0..1..1....0..0..1..1....1..1..1..1
..1..1..0..0....1..1..1..1....1..1..0..0....1..1..1..1....1..1..1..1
..1..1..0..0....1..1..0..0....1..1..0..0....1..1..2..2....1..1..1..1
..0..0..1..1....0..0..0..0....1..1..0..0....2..2..2..2....0..0..0..0
..0..0..1..1....0..0..0..0....1..1..0..0....2..2..2..2....0..0..0..0

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

Column 2 of A231227.

Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - 6*a(n-3) - 7*a(n-4) + 5*a(n-5) - a(n-6) + 6*a(n-7) + 17*a(n-8) - 20*a(n-9) - 2*a(n-10) + 4*a(n-11).

Empirical g.f.: x*(2 - 2*x - 8*x^2 - 3*x^3 + 16*x^4 + 5*x^6 + 19*x^7 - 34*x^8 - 2*x^9 + 8*x^10) / ((1 - x)*(1 - 2*x - 4*x^2 + 2*x^3 + 9*x^4 + 4*x^5 + 5*x^6 - x^7 - 18*x^8 + 2*x^9 + 4*x^10)). - Colin Barker, Sep 27 2018

A231222 Number of (n+2)X(3+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

3, 8, 21, 54, 185, 552, 1799, 5900, 19185, 63834, 210899, 701724, 2336721, 7786742, 25984043, 86721124, 289569291, 967130226, 3230474181, 10792263708, 36056118433, 120467821634, 402509354825, 1344900626136, 4493772713417

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 3 of A231227

			Some solutions for n=4
..0..0..0..0..0....0..0..1..1..1....0..0..0..1..1....0..0..1..1..1
..0..0..0..0..0....0..0..1..1..1....0..0..0..1..1....0..0..1..1..1
..1..1..1..1..1....1..1..0..0..0....0..0..0..1..1....0..0..0..1..1
..1..1..1..1..1....1..1..0..0..0....1..1..1..0..0....0..0..0..2..2
..0..0..0..0..0....1..1..0..0..0....1..1..1..0..0....0..0..2..2..2
..0..0..0..0..0....1..1..0..0..0....1..1..1..0..0....0..0..2..2..2

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

Empirical: a(n) = 3*a(n-1) +8*a(n-2) -18*a(n-3) -31*a(n-4) +39*a(n-5) +49*a(n-6) -73*a(n-7) +64*a(n-8) +15*a(n-9) -157*a(n-10) +98*a(n-11) +28*a(n-12) -24*a(n-13)

A231223 Number of (n+2)X(4+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

6, 17, 54, 182, 812, 2962, 12179, 50196, 205057, 864270, 3593492, 15094003, 63545858, 267204717, 1127304903, 4753575829, 20059305680, 84691952803, 357558971694, 1510077601850, 6377796652031, 26938452104661, 113791455759187

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 4 of A231227

			Some solutions for n=5
..0..0..0..0..1..1....0..0..0..0..0..0....0..0..1..1..1..1....0..0..0..1..1..1
..0..0..0..0..1..1....0..0..1..1..0..0....0..0..1..1..1..1....0..0..0..1..1..1
..0..0..0..1..1..1....1..1..1..1..1..1....0..0..0..1..1..1....0..0..0..0..1..1
..0..0..1..1..2..2....1..1..1..1..1..1....2..2..0..0..0..0....0..0..0..0..1..1
..1..1..1..2..2..2....2..2..1..1..1..1....2..2..2..0..0..0....0..0..1..1..0..0
..1..1..2..2..2..2....2..2..2..2..2..2....2..2..2..0..0..0....1..1..1..1..0..0
..1..1..2..2..2..2....2..2..2..2..2..2....2..2..2..0..0..0....1..1..1..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 96

Empirical recurrence of order 96 (see link above)

A231224 Number of (n+2)X(5+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

11, 45, 185, 812, 4298, 19935, 102113, 524113, 2687777, 14197596, 74308295, 393206009, 2088107591, 11086538469, 59103852278, 315153667732, 1682280633028, 8989204931719, 48042619335921, 256910321615776, 1374182610970469

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 5 of A231227

			Some solutions for n=5
..0..0..0..1..1..1..1....0..0..0..1..1..1..1....0..0..0..0..0..0..0
..0..0..0..1..1..1..1....0..0..0..1..1..1..1....0..0..0..0..0..0..0
..0..0..0..1..1..1..1....0..0..0..1..1..1..1....1..1..0..0..1..1..1
..2..2..0..0..1..1..1....0..0..0..1..1..1..1....1..1..1..1..1..1..1
..2..2..2..0..0..0..0....0..0..1..1..1..1..1....1..1..1..0..0..0..0
..2..2..2..2..0..0..0....1..1..1..1..1..1..1....1..1..0..0..0..0..0
..2..2..2..2..0..0..0....1..1..1..1..1..1..1....1..1..0..0..0..0..0

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

A231225 Number of (n+2)X(6+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

22, 103, 552, 2962, 19935, 117178, 748665, 4870988, 31483476, 210326324, 1392987995, 9318227740, 62685201542, 421269716690, 2844334077278, 19215230536497, 129923432463015, 879756395566799, 5958107153462019

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 6 of A231227

			Some solutions for n=4
..0..0..0..0..1..1..1..1....0..0..1..1..2..2..1..1....0..0..1..1..1..1..1..1
..0..0..0..0..1..1..1..1....0..0..1..1..2..2..1..1....0..0..1..1..1..1..1..1
..1..1..1..0..0..1..1..1....0..0..0..1..1..2..2..1....0..0..0..1..1..1..1..1
..1..1..1..1..0..0..1..1....0..0..0..1..1..2..2..1....0..0..0..2..2..1..1..1
..1..1..1..1..0..0..0..0....0..0..1..1..2..2..1..1....0..0..2..2..2..2..1..1
..1..1..1..1..0..0..0..0....0..0..1..1..2..2..1..1....0..0..2..2..2..2..1..1

R. H. Hardin, Table of n, a(n) for n = 1..74

A231226 Number of (n+2)X(7+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

43, 264, 1799, 12179, 102113, 748665, 5930126, 48317804, 390225796, 3267809753, 27184285056, 228686827731, 1938757497433, 16432432134267, 140079591842774, 1195812427594821, 10221439423090293, 87552309666153978, 750295493573918472

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 7 of A231227

			Some solutions for n=3
..0..0..1..1..1..1..1..0..0....0..0..0..0..0..0..1..1..1
..0..0..1..1..1..1..1..0..0....0..0..0..0..0..0..1..1..1
..0..0..1..1..1..1..1..0..0....2..2..0..0..0..0..1..1..1
..1..1..0..0..1..1..0..0..0....2..2..2..0..0..0..1..1..1
..1..1..0..0..0..0..0..0..0....2..2..2..0..0..0..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..31

A231220 Number of (n+2)X(n+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

1, 4, 21, 182, 4298, 117178, 5930126, 495739986

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Diagonal of A231227

			Some solutions for n=4
..0..0..0..0..0..0....0..0..0..1..1..1....0..0..0..0..1..1....0..0..0..1..1..1
..0..0..1..1..0..0....0..0..0..1..1..1....0..0..0..0..1..1....0..0..0..1..1..1
..1..1..1..1..1..1....1..1..1..0..0..0....0..0..0..0..1..1....0..0..1..1..1..1
..1..1..1..1..1..1....1..1..1..0..0..0....0..0..0..0..1..1....1..1..1..1..1..1
..2..2..2..2..2..2....0..0..0..1..1..1....0..0..0..0..1..1....1..1..1..1..1..1
..2..2..2..2..2..2....0..0..0..1..1..1....0..0..0..0..1..1....1..1..1..1..1..1

cp's OEIS Frontend

A231221 Number of (n+2) X (2+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231222 Number of (n+2)X(3+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231223 Number of (n+2)X(4+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231224 Number of (n+2)X(5+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231225 Number of (n+2)X(6+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231226 Number of (n+2)X(7+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231220 Number of (n+2)X(n+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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