A220579 -id:A220579 - cp's OEIS frontend

A220574 Equals one maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 n X 3 array.

4, 21, 91, 375, 1487, 5835, 22775, 88683, 344975, 1341395, 5214791, 20271307, 78797247, 306290211, 1190562423, 4627750267, 17988173039, 69920406547, 271782019879, 1056422029931, 4106332901663, 15961395217283, 62042250575063

Offset: 1

R. H. Hardin, Dec 16 2012

nonn

Column 3 of A220579.

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

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

Cf. A220579.

Empirical: a(n) = 3*a(n-1) + 4*a(n-2) + 2*a(n-3) - 12*a(n-4) - 16*a(n-5) for n>6.

Empirical g.f.: x*(4 + 9*x + 12*x^2 + 10*x^3 + 4*x^4 + 8*x^5) / (1 - 3*x - 4*x^2 - 2*x^3 + 12*x^4 + 16*x^5). - Colin Barker, Aug 01 2018

A220575 Equals one maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nX4 array.

Original entry on oeis.org

8, 115, 1441, 17505, 205323, 2352642, 26616961, 299065708, 3347252663, 37378135504, 416811197294, 4643851898712, 51709572437898, 575575826236700, 6405129188993734, 71266042324237205, 792848605905100847

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Column 4 of A220579

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

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

Empirical: a(n) = 49*a(n-1) -1058*a(n-2) +13352*a(n-3) -109857*a(n-4) +620213*a(n-5) -2449435*a(n-6) +6704400*a(n-7) -12020996*a(n-8) +11403651*a(n-9) +1989496*a(n-10) -18274416*a(n-11) +12779735*a(n-12) +13888615*a(n-13) -21466582*a(n-14) -4814175*a(n-15) +19770698*a(n-16) +1111627*a(n-17) -21069650*a(n-18) +16193684*a(n-19) -921063*a(n-20) -11095317*a(n-21) +11666405*a(n-22) -3274482*a(n-23) -1162160*a(n-24) +1220233*a(n-25) -1400204*a(n-26) +728140*a(n-27) -62411*a(n-28) +67213*a(n-29) -17664*a(n-30) -12975*a(n-31) -10189*a(n-32) +5572*a(n-33) -704*a(n-34) +256*a(n-35) for n>36

A220576 Equals one maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nX5 array.

Original entry on oeis.org

16, 371, 8334, 165130, 3162375, 59690533, 1120269376, 20961430054, 391477041024, 7301113014734, 136014086356403, 2531419892514045, 47074407789101798, 874763025888567980, 16244954731049984109, 301509938118179385606

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Column 5 of A220579

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

R. H. Hardin, Table of n, a(n) for n = 1..33

A220577 Equals one maps: number of n X 6 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 n X 6 array.

Original entry on oeis.org

32, 1504, 64497, 2652007, 106841503, 4239598056, 166807007000, 6529331189875, 254699982141104, 9910761556318406, 384907165469846911, 14926115051516165111, 578101882311226268847, 22367892146863380815542

Offset: 1

R. H. Hardin, Dec 16 2012

nonn

Column 6 of A220579.

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

R. H. Hardin, Table of n, a(n) for n = 1..17

Cf. A220579.

A220580 Equals one maps: number of 2Xn binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 2Xn array.

Original entry on oeis.org

1, 8, 21, 115, 371, 1504, 5240, 19904, 71787, 266591, 973703, 3590009, 13161398, 48409054, 177699822, 653013280, 2398088376, 8809799868, 32356803616, 118855121770, 436550962678, 1603501078153, 5889674104016, 21633105877502

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Row 2 of A220579

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

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

A220581 Equals one maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 3Xn array.

Original entry on oeis.org

1, 32, 91, 1441, 8334, 64497, 436288, 3036588, 21023792, 146254012, 1011489196, 7016643627, 48603225482, 336693889957, 2332461879768, 16156948253940, 111913294295697, 775187951935208, 5369332881497134, 37190288381188178

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Row 3 of A220579

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

R. H. Hardin, Table of n, a(n) for n = 1..27

A220573 Equals one maps: number of n X n binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 n X n array.

Original entry on oeis.org

1, 8, 91, 17505, 3162375, 4239598056, 12835487766480

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Diagonal of A220579

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

A220578 Equals one maps: number of nX7 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nX7 array.

Original entry on oeis.org

64, 5240, 436288, 33180533, 2449921734, 178051989526, 12835487766480

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Column 7 of A220579

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

A220582 Equals one maps: number of 4Xn binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 4Xn array.

Original entry on oeis.org

1, 128, 375, 17505, 165130, 2652007, 33180533, 450926562, 5905274893, 77665021467

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Row 4 of A220579

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

A220583 Equals one maps: number of 5Xn binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 5Xn array.

Original entry on oeis.org

1, 512, 1487, 205323, 3162375, 106841503, 2449921734, 65126683335

Offset: 1

R. H. Hardin Dec 16 2012

nonn

Row 5 of A220579

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

cp's OEIS Frontend

A220574 Equals one maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 n X 3 array.

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A220575 Equals one maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nX4 array.

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A220576 Equals one maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nX5 array.

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A220577 Equals one maps: number of n X 6 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 n X 6 array.

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A220580 Equals one maps: number of 2Xn binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 2Xn array.

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A220581 Equals one maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 3Xn array.

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A220573 Equals one maps: number of n X n binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 n X n array.

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A220578 Equals one maps: number of nX7 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 nX7 array.

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A220582 Equals one maps: number of 4Xn binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 4Xn array.

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Examples

A220583 Equals one maps: number of 5Xn binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal and antidiagonal neighbors in a random 0..1 5Xn array.

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