A228660 -id:A228660 - cp's OEIS frontend

A228654 Number of n X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

1, 2, 34, 416, 24109, 1482892, 337258048, 99770848656, 92600434253746, 128571982215641568, 497887042842429868023, 3189515020018986830642404, 52334113476786453501159739264, 1527284319716267796002249895255726

Offset: 1

R. H. Hardin Aug 29 2013

nonn

Diagonal of A228660

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

R. H. Hardin, Table of n, a(n) for n = 1..29

A228655 Number of nX3 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

2, 8, 34, 140, 574, 2348, 9598, 39224, 160282, 654944, 2676202, 10935332, 44683222, 182581508, 746051878, 3048465200, 12456425842, 50898577976, 207978216754, 849826072316, 3472499977390, 14189087019740, 57978456949582

Offset: 1

R. H. Hardin Aug 29 2013

nonn

Column 3 of A228660

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

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

Empirical: a(n) = 5*a(n-1) -3*a(n-2) -3*a(n-3).

Empirical: G.f. -2*x*(-1+x) / ( 1-5*x+3*x^2+3*x^3 ). - R. J. Mathar, Aug 29 2013

A228656 Number of nX4 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

3, 14, 78, 416, 2228, 11912, 63688, 340480, 1820208, 9730784, 52020448, 278099456, 1486709568, 7947894912, 42489154688, 227145461760, 1214311301888, 6491663650304, 34704195603968, 185527355908096, 991822435038208

Offset: 1

R. H. Hardin Aug 29 2013

nonn

Column 4 of A228660

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

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

Empirical: a(n) = 6*a(n-1) -2*a(n-2) -8*a(n-3).

Empirical: G.f. -x*(-3+4*x) / ( 1-6*x+2*x^2+8*x^3 ). - R. J. Mathar, Aug 29 2013

A228657 Number of n X 5 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

5, 38, 335, 2844, 24109, 203762, 1720343, 14516920, 122469941, 1033083774, 8714026943, 73500740436, 619954240797, 5229079954762, 44105207907655, 372009451809136, 3137746452123621, 26465592072488918, 223226285220003247

Offset: 1

R. H. Hardin, Aug 29 2013

nonn

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

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

Column 5 of A228660.

Empirical: a(n) = 12*a(n-1) - 27*a(n-2) - 32*a(n-3) + 49*a(n-4) + 20*a(n-5) - 5*a(n-6).

Empirical g.f.: x*(5 - 22*x + 14*x^2 + 10*x^3 - 3*x^4) / (1 - 12*x + 27*x^2 + 32*x^3 - 49*x^4 - 20*x^5 + 5*x^6). - Colin Barker, Sep 12 2018

A228658 Number of n X 6 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

8, 80, 968, 11148, 128740, 1482892, 17074988, 196565912, 2262692928, 26045341080, 299798763232, 3450863834052, 39721453897148, 457216814726132, 5262827734777604, 60578160174884624, 697289282211813816

Offset: 1

R. H. Hardin, Aug 29 2013

nonn

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

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

Column 6 of A228660.

Empirical: a(n) = 14*a(n-1) - 17*a(n-2) - 142*a(n-3) + 59*a(n-4) + 352*a(n-5) + 103*a(n-6) - 48*a(n-7).

Empirical g.f.: 4*x*(2 - 8*x - 4*x^2 + 23*x^3 + 3*x^4 - 8*x^5) / (1 - 14*x + 17*x^2 + 142*x^3 - 59*x^4 - 352*x^5 - 103*x^6 + 48*x^7). - Colin Barker, Sep 12 2018

A228659 Number of nX7 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

13, 194, 3556, 62368, 1096624, 19236832, 337258048, 5910459096, 103561279328, 1814380139952, 31785935283840, 556837728488064, 9754730426036000, 170882696555044928, 2993497165464775680, 52439495408779417216

Offset: 1

R. H. Hardin Aug 29 2013

nonn

Column 7 of A228660

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

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

Empirical: a(n) = 30*a(n-1) -226*a(n-2) -108*a(n-3) +4324*a(n-4) -1612*a(n-5) -27016*a(n-6) -2240*a(n-7) +50112*a(n-8) +20032*a(n-9) -16768*a(n-10) -4864*a(n-11) +2048*a(n-12)

A228661 Number of 2 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

2, 2, 8, 14, 38, 80, 194, 434, 1016, 2318, 5366, 12320, 28418, 65378, 150632, 346766, 798662, 1838960, 4234946, 9751826, 22456664, 51712142, 119082134, 274218560, 631464962, 1454120642, 3348515528, 7710877454, 17756424038, 40889056400

Offset: 1

R. H. Hardin, Aug 29 2013

nonn

Row 2 of A228660.

The recurrence is demonstrated as follows: For every 2X(n-1) array, we can add the column (0,0) to get an appropriate array of size 2Xn, and for every 2X(n-2) array, we can add the column (0,0) and either (1,0), (0,1) or (1,1) to get an appropriate sized array. Every admissible array is of one of these two forms, and these two forms do not overlap (since their last columns are different). - Tom Edgar, Aug 29 2013

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

R. H. Hardin, Table of n, a(n) for n = 1..210
Index entries for linear recurrences with constant coefficients, signature (1,3).

a(n) = a(n-1) +3*a(n-2).
G.f.: -2*x / ( -1+x+3*x^2 ). a(n) = 2*A006130(n-1). - R. J. Mathar, Aug 29 2013
a(n) = -2/13*sqrt(13)*(-1/2*sqrt(13)+1/2)^n + 2/13*sqrt(13)*(1/2*sqrt(13)+1/2)^n. - Tom Edgar, Aug 31 2013
G.f.: Q(0)/x -1/x, where Q(k) = 1 + 3*x^2 + (2*k+3)*x - x*(2*k+1 + 3*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 05 2013

A228662 Number of 3 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

4, 5, 34, 78, 335, 968, 3556, 11245, 38986, 127662, 433015, 1437072, 4833924, 16125205, 54068594, 180718798, 605223135, 2024416088, 6776576996, 22673534845, 75884451226, 253927226542, 849793486215, 2843728075552, 9516580935684

Offset: 1

R. H. Hardin, Aug 29 2013

nonn

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

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

Row 3 of A228660.

Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - 5*a(n-3).

Empirical g.f.: x*(4 - 3*x) / (1 - 2*x - 6*x^2 + 5*x^3). - Colin Barker, Sep 12 2018

A228663 Number of 4 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

8, 12, 140, 416, 2844, 11148, 62368, 275708, 1420076, 6614240, 32897116, 156718796, 767930400, 3694025404, 17985757548, 86879470432, 421850136604, 2041379040012, 9900460336800, 47946203889788, 232416817429420, 1125924852017632

Offset: 1

R. H. Hardin, Aug 29 2013

nonn

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

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

Row 4 of A228660.

Empirical: a(n) = 2*a(n-1) + 16*a(n-2) - 7*a(n-3) - 18*a(n-4).

Empirical g.f.: 4*x*(1 + x)*(2 - 3*x) / (1 - 2*x - 16*x^2 + 7*x^3 + 18*x^4). - Colin Barker, Sep 12 2018

A228664 Number of 5 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

Original entry on oeis.org

16, 29, 574, 2228, 24109, 128740, 1096624, 6780585, 51990406, 344168764, 2516149353, 17192729316, 122982062328, 852741876277, 6038989672654, 42158071124804, 297183800090933, 2081125389730084, 14639300678885312

Offset: 1

R. H. Hardin, Aug 29 2013

nonn

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

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

Row 5 of A228660.

Empirical: a(n) = 4*a(n-1) + 34*a(n-2) - 76*a(n-3) - 134*a(n-4) + 258*a(n-5) + 45*a(n-6) - 102*a(n-7).

Empirical g.f.: x*(16 - 35*x - 86*x^2 + 162*x^3 + 29*x^4 - 66*x^5) / (1 - 4*x - 34*x^2 + 76*x^3 + 134*x^4 - 258*x^5 - 45*x^6 + 102*x^7). - Colin Barker, Sep 12 2018

cp's OEIS Frontend

A228654 Number of n X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228655 Number of nX3 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228656 Number of nX4 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228657 Number of n X 5 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228658 Number of n X 6 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228659 Number of nX7 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228661 Number of 2 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228662 Number of 3 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228663 Number of 4 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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A228664 Number of 5 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

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