A231219 -id:A231219 - cp's OEIS frontend

A231213 Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

4, 9, 22, 59, 156, 413, 1098, 2919, 7760, 20633, 54862, 145875, 387876, 1031349, 2742322, 7291743, 19388504, 51553393, 137078774, 364487947, 969161452, 2576968397, 6852074138, 18219439575, 48444890080, 128813368009, 342510505246

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

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

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

Column 2 of A231219.

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

Empirical g.f.: x*(4 - 3*x - x^2 - 2*x^3) / ((1 - x)*(1 - 2*x - x^2 - 2*x^3)). - Colin Barker, Sep 27 2018

A231214 Number of (n+1)X(3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

7, 22, 93, 408, 1793, 7844, 34609, 152421, 672446, 2965705, 13084976, 57727896, 254711179, 1123832479, 4958718969, 21879386505, 96539467026, 425965183425, 1879509395614, 8293059346003, 36591936428964, 161456668184975

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 3 of A231219

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

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

Empirical: a(n) = 8*a(n-1) -16*a(n-2) -11*a(n-3) +77*a(n-4) -147*a(n-5) +179*a(n-6) -109*a(n-7) +129*a(n-8) -231*a(n-9) +327*a(n-10) -280*a(n-11) -288*a(n-12) +548*a(n-13) -504*a(n-14) +486*a(n-15) -183*a(n-16) +48*a(n-17) -24*a(n-18) -8*a(n-19)

A231215 Number of (n+1) X (4+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

12, 59, 408, 2892, 20027, 139438, 969461, 6745110, 46938804, 326645650, 2273218682, 15819608975, 110091246193, 766140117967, 5331683762978, 37103974744989, 258212125773531, 1796936761480570, 12505151919361622

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 4 of A231219.

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

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

Cf. A231219.

Empirical recurrence of order 68 (see link above).

A231216 Number of (n+1)X(5+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

23, 156, 1793, 20027, 226764, 2534951, 28439115, 318236849, 3565691309, 39935313475, 447387885717, 5011544754282, 56140525034274, 628886833447925, 7044850137852253, 78916780609087401, 884031405098540067

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 5 of A231219

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

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

A231217 Number of (n+1)X(6+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

44, 413, 7844, 139438, 2534951, 45593903, 820418528, 14743946094, 265057746273, 4764850607558, 85665969646863, 1540161104743915, 27690540964980741, 497845771876658529, 8950739306626864235, 160924591529710020492

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 6 of A231219

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

R. H. Hardin, Table of n, a(n) for n = 1..85

A231218 Number of (n+1)X(7+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

87, 1098, 34609, 969461, 28439115, 820418528, 23748656906, 685733582035, 19812622781057, 572302029497356, 16533962109257389, 477663753823928105, 13800046313373114629, 398691931165963350492, 11518505348614958772694

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Column 7 of A231219

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

R. H. Hardin, Table of n, a(n) for n = 1..18

A231212 Number of (n+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

3, 9, 93, 2892, 226764, 45593903, 23748656906, 31822302958042

Offset: 1

R. H. Hardin, Nov 05 2013

nonn

Diagonal of A231219

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

cp's OEIS Frontend

A231213 Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

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A231214 Number of (n+1)X(3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

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A231215 Number of (n+1) X (4+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

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A231216 Number of (n+1)X(5+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

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A231217 Number of (n+1)X(6+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

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A231218 Number of (n+1)X(7+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

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A231212 Number of (n+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

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