A208069 -id:A208069 - cp's OEIS frontend

A208063 Number of n X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

2, 16, 72, 576, 3696, 26244, 198000, 1638400, 12913840, 117722500, 1052059680, 10059287616, 97769309736, 1020075760144, 10507456855392, 116747852120064, 1295601058976256, 15148523442518244, 177995312325281880

Offset: 1

R. H. Hardin Feb 23 2012

nonn

Diagonal of A208069

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

R. H. Hardin, Table of n, a(n) for n = 1..32

A208064 Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

6, 36, 72, 144, 216, 324, 432, 576, 720, 900, 1080, 1296, 1512, 1764, 2016, 2304, 2592, 2916, 3240, 3600, 3960, 4356, 4752, 5184, 5616, 6084, 6552, 7056, 7560, 8100, 8640, 9216, 9792, 10404, 11016, 11664, 12312, 12996, 13680, 14400, 15120, 15876, 16632

Offset: 1

R. H. Hardin, Feb 23 2012

nonn

Column 3 of A208069.

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

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

Cf. A208069.

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>5.
Conjectures from Colin Barker, Jun 27 2018: (Start)
G.f.: 6*x*(1 + 4*x + 2*x^3 - x^4) / ((1 - x)^3*(1 + x)).
a(n) = 9*n^2 for n>1 and even.
a(n) = 9*n^2-9 for n>1 and odd.
(End)

A208065 Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

10, 100, 240, 576, 1008, 1764, 2688, 4096, 5760, 8100, 10800, 14400, 18480, 23716, 29568, 36864, 44928, 54756, 65520, 78400, 92400, 108900, 126720, 147456, 169728, 195364, 222768, 254016, 287280, 324900, 364800, 409600, 456960, 509796, 565488

Offset: 1

R. H. Hardin, Feb 23 2012

nonn

Column 4 of A208069.

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

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

Cf. A208069.

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n>9.
Conjectures from Colin Barker, Jun 27 2018: (Start)
G.f.: 2*x*(5 + 40*x + 10*x^2 - 22*x^3 - 12*x^4 - 12*x^5 + 10*x^6 + 10*x^7 - 5*x^8) / ((1 - x)^5*(1 + x)^3).
a(n) = n^2*(n + 8)^2/4 for n>1 and even.
a(n) = (n - 1)*(n + 1)*(n + 7)*(n + 9)/4 for n>1 and odd.
(End)

A208066 Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

16, 256, 704, 1936, 3696, 7056, 11424, 18496, 27200, 40000, 55200, 76176, 100464, 132496, 168896, 215296, 267264, 331776, 403200, 490000, 585200, 698896, 822624, 968256, 1125696, 1308736, 1505504, 1731856, 1974000, 2250000, 2544000, 2876416

Offset: 1

R. H. Hardin, Feb 23 2012

nonn

Column 5 of A208069.

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

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

Cf. A208069.

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n>9.

Empirical g.f.: 16*x*(1 + 14*x + 10*x^2 + 7*x^3 - 3*x^4 - 5*x^5 + 2*x^6 + 2*x^7 - x^8) / ((1 - x)^5*(1 + x)^3). - Colin Barker, Jun 27 2018

A208067 Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

26, 676, 2080, 6400, 12960, 26244, 44064, 73984, 111520, 168100, 236160, 331776, 443520, 592900, 763840, 984064, 1232064, 1542564, 1887840, 2310400, 2775520, 3334276, 3944160, 4665600, 5447520, 6360484, 7344064, 8479744, 9696960

Offset: 1

R. H. Hardin, Feb 23 2012

nonn

Column 6 of A208069.

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

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

Cf. A208069.

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n>9.

Empirical g.f.: 2*x*(13 + 312*x + 338*x^2 + 522*x^3 + 28*x^4 - 76*x^5 + 26*x^6 + 26*x^7 - 13*x^8) / ((1 - x)^5*(1 + x)^3). - Colin Barker, Jun 27 2018

A208068 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

42, 1764, 6216, 21904, 48840, 108900, 198000, 360000, 582000, 940900, 1408440, 2108304, 2988216, 4235364, 5762400, 7840000, 10332000, 13616100, 17490600, 22467600, 28259880, 35545444, 43928016, 54287424, 66090960, 80460900, 96696600

Offset: 1

R. H. Hardin, Feb 23 2012

nonn

Column 7 of A208069.

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

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

Cf. A208069.

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) - 5*a(n-4) + 20*a(n-5) - 20*a(n-7) + 5*a(n-8) + 10*a(n-9) - 4*a(n-10) - 2*a(n-11) + a(n-12) for n>13.

Empirical g.f.: 2*x*(21 + 840*x + 1260*x^2 + 1418*x^3 - 991*x^4 - 3128*x^5 - 160*x^6 + 1420*x^7 + 95*x^8 - 160*x^9 + 84*x^10 + 42*x^11 - 21*x^12) / ((1 - x)^7*(1 + x)^5). - Colin Barker, Jun 27 2018

A208070 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

12, 144, 216, 1008, 3696, 12960, 48840, 179520, 657000, 2423280, 8913456, 32769360, 120581784, 443565696, 1631571912, 6002079552, 22079078352, 81218792016, 298770650040, 1099049754720, 4042930839192, 14872226620512, 54708578740752

Offset: 1

R. H. Hardin, Feb 23 2012

nonn

Row 5 of A208069.

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

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

Cf. A208069.

Empirical: a(n) = a(n-1) + 4*a(n-2) + 19*a(n-3) + 10*a(n-4) + 5*a(n-5) - 27*a(n-6) - 2*a(n-7) - 4*a(n-8) + 8*a(n-9) for n>11.

Empirical g.f.: 12*x*(1 + 11*x + 2*x^2 - x^3 - 86*x^4 - 31*x^5 - 51*x^6 + 114*x^7 + 4*x^8 + 24*x^9 - 32*x^10) / ((1 - 2*x - 4*x^2 - 8*x^3)*(1 + x + 2*x^2 - 3*x^3 - x^5 + x^6)). - Colin Barker, Jun 27 2018

A208071 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

16, 256, 324, 1764, 7056, 26244, 108900, 435600, 1726596, 6937956, 27751824, 110880900, 443776356, 1775105424, 7099410564, 28399664484, 113598657936, 454386542724, 1817562348900, 7270249395600, 29080932870276, 116323860905316

Offset: 1

R. H. Hardin, Feb 23 2012

nonn

Row 6 of A208069.

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

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

Cf. A208069.

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 17*a(n-3) - 2*a(n-4) - 4*a(n-5) - 16*a(n-6) for n>8.

Empirical g.f.: 4*x*(4 + 56*x - 63*x^2 - 45*x^3 - 522*x^4 + 36*x^5 + 32*x^6 + 448*x^7) / ((1 - x)*(1 - 4*x)*(1 + x + x^2)*(1 + 2*x + 4*x^2)). - Colin Barker, Jun 27 2018

A208072 Number of 7Xn 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

20, 400, 432, 2688, 11424, 44064, 198000, 844800, 3542544, 15213984, 64859616, 275633280, 1175819856, 5010674496, 21340192176, 90942560256, 387500834976, 1650940063776, 7034502996720, 29972774288640, 127706156346384

Offset: 1

R. H. Hardin Feb 23 2012

nonn

Row 7 of A208069

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

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

Empirical: a(n) = a(n-1) +4*a(n-2) +39*a(n-3) +20*a(n-4) +19*a(n-5) -191*a(n-6) -42*a(n-7) -36*a(n-8) +216*a(n-9) for n>11

cp's OEIS Frontend

A208063 Number of n X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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A208064 Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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A208065 Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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A208066 Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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A208067 Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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A208068 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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A208070 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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A208071 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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A208072 Number of 7Xn 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

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