A189343 -id:A189343 - cp's OEIS frontend

A189336 Number of nX2 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

4, 16, 64, 225, 784, 2704, 9409, 32761, 114244, 398161, 1387684, 4835601, 16851025, 58721569, 204633025, 713103616, 2485022500, 8659791364, 30177596089, 105162706944, 366470415424, 1277074025929, 4450340433889, 15508521343396

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 2 of A189343

			Some solutions for 4X2
..0..0....1..0....1..0....0..0....1..0....0..1....0..0....0..1....1..1....0..0
..1..1....1..0....0..0....1..0....1..0....0..1....1..1....1..0....0..1....1..1
..0..0....1..0....1..0....0..1....0..1....0..1....1..0....0..1....1..0....1..1
..0..1....0..1....1..1....0..1....1..1....0..0....0..1....1..0....0..1....1..1

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

A049864(n+2) squared

Empirical: a(n) = 4*a(n-1) -a(n-2) -6*a(n-3) +12*a(n-4) -3*a(n-5) +3*a(n-6) -6*a(n-7) +a(n-8) -a(n-9) +a(n-10)

A189337 Number of nX3 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

8, 64, 512, 3375, 21952, 140608, 912673, 5929741, 38614472, 251239591, 1634691752, 10633486599, 69173457625, 449983383247, 2927275422625, 19042718961664, 123878371625000, 805862864751112, 5242361459792813, 34103003909455872

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 3 of A189343

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

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

A049864(n+2) cubed

Empirical: a(n) = 7*a(n-1) -41*a(n-3) +130*a(n-4) +81*a(n-6) -369*a(n-7) -73*a(n-8) -173*a(n-9) +243*a(n-10) +211*a(n-11) -77*a(n-12) +117*a(n-13) +81*a(n-14) +20*a(n-16) +13*a(n-17) +a(n-19) +a(n-20)

A189339 Number of nX5 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

28, 784, 21952, 390721, 6814820, 109746642, 1857004061, 31177656076, 533269057178, 9053472938552, 154252966185542, 2618674812680579, 44520074517291894, 756141322418868556, 12851400623635035810

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 5 of A189343

			Some solutions for 4X5
..0..0..1..0..0....0..1..1..0..1....0..0..1..1..0....0..0..0..0..0
..0..1..0..1..0....0..0..0..1..1....0..1..1..1..1....0..1..1..1..0
..1..0..1..1..0....0..0..1..1..1....0..0..0..0..1....0..0..0..1..0
..0..0..1..0..1....0..0..1..0..1....1..0..1..0..0....0..1..1..0..1

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

A189338 Number of nX4 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

15, 225, 3375, 36626, 390721, 3988168, 42069350, 442969881, 4709354541, 49857094654, 528436125424, 5591212296038, 59196669906872, 626540356943069, 6633322246811551, 70220475509151710, 743409267344795743

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 4 of A189343

			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..0..1..0....0..0..1..0....0..0..1..0....0..1..1..0....0..0..0..0
..1..0..0..0....0..0..1..1....0..1..0..1....0..0..1..0....0..0..0..1
..0..0..1..0....0..1..0..0....1..0..1..0....1..1..1..0....0..1..1..0
..0..0..0..0....1..1..0..0....1..1..0..1....1..1..0..0....0..0..0..0

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

A189340 Number of n X 6 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

52, 2704, 140608, 3988168, 109746642, 2650369322, 68439605144, 1732402041622, 45288523287014, 1169200527259744, 30459419241960870, 788089712516187485, 20460101431991974234, 529811400562012142385, 13741195617567627797520

Offset: 1

R. H. Hardin, Apr 20 2011

nonn

Column 6 of A189343.

			Some solutions for 4 X 6:
..0..0..0..1..1..0....0..0..0..0..1..0....0..0..0..0..1..0....0..0..1..1..0..1
..0..0..1..0..0..0....0..0..1..1..1..1....0..0..0..1..0..1....0..0..0..1..1..0
..0..1..1..1..0..1....0..1..1..1..0..1....0..0..1..1..0..1....0..1..1..1..0..1
..0..0..0..1..0..1....0..0..0..1..1..0....0..1..0..0..0..1....0..0..0..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..116

A189341 Number of nX7 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

97, 9409, 912673, 42069350, 1857004061, 68439605144, 2739456017053, 106150557957909, 4311950202672542, 172004809421325314, 6968408164659864073, 279225921295911354381, 11255564881813924496670, 451571763353227520521337

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 7 of A189343

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

R. H. Hardin, Table of n, a(n) for n = 1..24

A189335 Number of n X n binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

2, 16, 512, 36626, 6814820, 2650369322, 2739456017053, 6190300153637745

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Diagonal of A189343

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

A189342 Number of nX8 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

181, 32761, 5929741, 442969881, 31177656076, 1732402041622, 106150557957909, 6190300153637745

Offset: 1

R. H. Hardin Apr 20 2011

nonn

Column 8 of A189343

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

cp's OEIS Frontend

A189336 Number of nX2 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

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A189337 Number of nX3 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

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A189339 Number of nX5 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

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A189338 Number of nX4 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

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A189340 Number of n X 6 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

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A189341 Number of nX7 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

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A189335 Number of n X n binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

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A189342 Number of nX8 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally.

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