A181224 -id:A181224 - cp's OEIS frontend

A181219 Number of nX3 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

7, 49, 230, 1209, 6475, 34020, 179097, 944514, 4978956, 26241679, 138316703, 729070278, 3842881010, 20255521442, 106765644778, 562755120940, 2966245831625, 15634892911279, 82410528967137, 434380653636920

Offset: 1

R. H. Hardin Oct 10 2010

nonn

Column 3 of A181224

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

R. H. Hardin, Table of n, a(n) for n=1..350

Empirical: a(n)=2*a(n-1)+8*a(n-2)+38*a(n-3)+51*a(n-4)+41*a(n-5)-48*a(n-6)-88*a(n-7)-4*a(n-8)-8*a(n-9)-15*a(n-10)+14*a(n-11)-7*a(n-12)+a(n-13)-2*a(n-14)

A181220 Number of n X 4 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

Original entry on oeis.org

13, 169, 1209, 10732, 97764, 845531, 7426986, 65480503, 574725752, 5050028956, 44391722285, 390072820213, 3427866363455, 30124436697657, 264728435711181, 2326400950974628, 20444198985083330, 179661312288590309

Offset: 1

R. H. Hardin Oct 10 2010

nonn

Column 4 of A181224.

			Some avoided solutions for 3 X 4
..0..1..0..1....1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..1
..0..0..1..0....1..0..0..0....0..0..1..1....0..1..0..0....0..1..0..1
..0..1..0..0....1..1..0..0....0..0..1..0....1..0..1..0....0..0..0..1

R. H. Hardin, Table of n, a(n) for n=1..275

Cf. A181224.

Empirical: a(n)=4*a(n-1)+27*a(n-2)+150*a(n-3)-59*a(n-4)-656*a(n-5)-2090*a(n-6)+4600*a(n-7)+558*a(n-8)-6222*a(n-9)+6935*a(n-10)-36512*a(n-11)+93343*a(n-12)-70961*a(n-13)+82681*a(n-14)-47047*a(n-15)-247244*a(n-16)+404537*a(n-17)-466677*a(n-18)+482071*a(n-19)-352513*a(n-20)+295888*a(n-21)-133016*a(n-22)+13672*a(n-23)-34436*a(n-24)+7664*a(n-25)+7816*a(n-26)+108*a(n-27)-620*a(n-28)-1024*a(n-29)+144*a(n-30)+32*a(n-31)+48*a(n-32).

A181221 Number of nX5 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

Original entry on oeis.org

24, 576, 6475, 97764, 1495392, 21513936, 316896477, 4672517426, 68571093673, 1008146803248, 14823077688569, 217869625616208, 3202690847200999, 47079980407589036, 692062815855417554, 10173239318638447266

Offset: 1

R. H. Hardin Oct 10 2010

nonn

Column 5 of A181224

			Some avoided solutions for 3X5
..0..1..0..0..0....0..1..0..0..0....0..0..0..0..0....0..0..0..0..1
..0..0..1..0..0....0..1..0..0..0....0..0..0..0..0....0..0..0..1..0
..1..0..0..1..0....0..1..0..1..0....1..1..1..1..0....1..0..1..0..0

R. H. Hardin, Table of n, a(n) for n=1..225

A181222 Number of nX6 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

Original entry on oeis.org

44, 1936, 34020, 845531, 21513936, 507962194, 12297765846, 298705742479, 7214603356059, 174532135006271, 4223718879095262, 102172834596986892, 2471821868183143126, 59801751244062857757, 1446764589780206695039

Offset: 1

R. H. Hardin Oct 10 2010

nonn

Column 6 of A181224

			Some avoided solutions for 3X6
..0..0..0..1..1..0....0..0..0..0..1..0....1..0..1..1..1..0....0..1..0..0..0..0
..0..0..1..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..1..1..0..0
..0..1..0..0..0..0....0..0..1..1..1..0....0..0..0..0..0..0....0..0..0..1..0..0

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

A181223 Number of nX7 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

Original entry on oeis.org

81, 6561, 179097, 7426986, 316896477, 12297765846, 493466099722, 19886730240632, 794878208506289, 31852650059853831, 1277093175893680596, 51166967011661264756, 2050407503529684003122, 82170493913101130433607

Offset: 1

R. H. Hardin Oct 10 2010

nonn

Column 7 of A181224

			Some avoided solutions for 3X7
..1..0..0..0..0..1..0....0..0..0..0..0..0..0....0..1..0..1..0..0..0
..1..0..0..0..0..0..0....1..1..1..0..0..0..0....0..0..0..0..1..0..0
..1..0..0..0..0..0..0....1..0..0..0..0..0..0....0..0..0..0..0..1..0

R. H. Hardin, Table of n, a(n) for n=1..175

A181218 Number of n X n binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

Original entry on oeis.org

2, 16, 230, 10732, 1495392, 507962194, 493466099722, 1328921689649459, 9633695407844528952, 192630734231370260714836, 10572973250296811381776668634

Offset: 1

R. H. Hardin Oct 10 2010

nonn

Diagonal of A181224

			Some avoided solutions for 3X3
..1..1..1....1..0..0....0..0..1....1..1..1....1..0..0....1..1..0....1..0..0
..0..0..0....0..1..1....0..1..0....0..0..1....0..0..0....0..1..0....1..0..0
..0..0..1....0..0..1....1..0..1....0..0..0....1..1..1....0..0..1....1..1..0

cp's OEIS Frontend

A181219 Number of nX3 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

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A181220 Number of n X 4 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

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A181221 Number of nX5 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

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A181222 Number of nX6 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

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A181223 Number of nX7 binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

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A181218 Number of n X n binary matrices with no three 1's adjacent in a line horizontally, vertically, diagonally or antidiagonally.

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