A208840 -id:A208840 - cp's OEIS frontend

A208836 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

10, 100, 282, 855, 3010, 11242, 44275, 179032, 737550, 3070375, 12868830, 54154926, 228475507, 965411356, 4083220786, 17280246775, 73157026602, 309784875682, 1311973439667, 5556832891632, 23537091290566, 99699402777415

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Column 4 of A208840.

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

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

Cf. A208840.

Empirical: a(n) = 7*a(n-1) - 8*a(n-2) - 27*a(n-3) + 45*a(n-4) + 24*a(n-5) - 51*a(n-6) - 3*a(n-7) + 16*a(n-8) - a(n-9) - a(n-10) for n>11.

Empirical g.f.: x*(10 + 30*x - 338*x^2 - 49*x^3 + 1531*x^4 - 114*x^5 - 1834*x^6 + 200*x^7 + 612*x^8 - 63*x^9 - 41*x^10) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 + x - x^2)*(1 - x - x^2)*(1 - 4*x - x^2)). - Colin Barker, Mar 07 2018

A208838 Number of nX6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

26, 676, 2430, 9801, 49126, 272206, 1644265, 10399480, 67895010, 451450105, 3037317426, 20579585922, 140057351785, 955762122172, 6533166024022, 44704031815465, 306089086744206, 2096624267502790, 14364797790087081

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Column 6 of A208840

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

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

Empirical: a(n) = 11*a(n-1) -17*a(n-2) -124*a(n-3) +276*a(n-4) +396*a(n-5) -902*a(n-6) -462*a(n-7) +946*a(n-8) +220*a(n-9) -340*a(n-10) -44*a(n-11) +39*a(n-12) +3*a(n-13) -a(n-14) for n>15

A208835 Number of n X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 16, 78, 855, 8736, 272206, 6206445, 613538688, 30091441770, 9949962265465, 995860712362464, 1146808937112275178, 223896318271083352427, 927305041435819383020944, 341298409330345173624970966

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Diagonal of A208840

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

R. H. Hardin, Table of n, a(n) for n = 1..37

A208837 Number of nX5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

16, 256, 768, 2421, 8736, 33088, 131355, 533568, 2203920, 9189085, 38550096, 162319248, 685048923, 2895251008, 12247097568, 51834040005, 219453561408, 929308800928, 3935800405563, 16670184835968, 70610452390128

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Column 5 of A208840

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

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

Empirical: a(n) = 7*a(n-1) -8*a(n-2) -27*a(n-3) +45*a(n-4) +24*a(n-5) -51*a(n-6) -3*a(n-7) +16*a(n-8) -a(n-9) -a(n-10) for n>11

A208839 Number of nX7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

42, 1764, 7086, 31419, 169974, 992574, 6206445, 40122936, 265568130, 1780946115, 12045557394, 81883111842, 558396389421, 3815311552572, 26099962612902, 178677791790795, 1223770846004094, 8384018150245206, 57448693695345549

Offset: 1

R. H. Hardin Mar 01 2012

nonn

Column 7 of A208840

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

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

Empirical: a(n) = 11*a(n-1) -17*a(n-2) -124*a(n-3) +276*a(n-4) +396*a(n-5) -902*a(n-6) -462*a(n-7) +946*a(n-8) +220*a(n-9) -340*a(n-10) -44*a(n-11) +39*a(n-12) +3*a(n-13) -a(n-14) for n>15

A208841 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

9, 81, 171, 855, 2421, 9801, 31419, 116919, 394965, 1419849, 4902939, 17375031, 60551541, 213310665, 746231931, 2622329271, 9188418069, 32255749449, 113096449755, 396852637239, 1391845926069, 4883081614281, 17127968887611

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 4 of A208840.

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

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

Cf. A208840.

Empirical: a(n) = 2*a(n-1) +7*a(n-2) -6*a(n-3).

A208842 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

14, 196, 406, 3010, 8736, 49126, 169974, 833364, 3166030, 14462714, 57750784, 254227806, 1042375166, 4500225380, 18712446886, 79961471506, 334969826464, 1423640395254, 5987342521510, 25373701694964, 106935469300254

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 5 of A208840.

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

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

Cf. A208840.

Empirical: a(n) = 2*a(n-1) + 12*a(n-2) - 11*a(n-3).

Empirical g.f.: 14*x*(1 + 12*x - 11*x^2) / (1 - 2*x - 12*x^2 + 11*x^3). - Colin Barker, Jul 07 2018

A208843 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

22, 484, 990, 11242, 33088, 272206, 992574, 6800596, 28280758, 173714530, 783832896, 4504621990, 21385325830, 117970266436, 578059231662, 3109202601274, 15538154773504, 82277236170910, 416242718387694

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 6 of A208840.

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

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

Cf. A208840.

Empirical: a(n) = 2*a(n-1) + 20*a(n-2) - 19*a(n-3).

Empirical g.f.: 22*x*(1 + 20*x - 19*x^2) / (1 - 2*x - 20*x^2 + 19*x^3). - Colin Barker, Jul 07 2018

A208844 Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

35, 1225, 2485, 44275, 131355, 1644265, 6206445, 62470275, 277136755, 2417186345, 11980836805, 94860446835, 507738545195, 3762485058185, 21244807809085, 150403989092035, 881487114021955, 6046472018190345, 36369091148160085

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Row 7 of A208840.

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

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

Cf. A208840.

Empirical: a(n) = 2*a(n-1) + 33*a(n-2) - 32*a(n-3).

Empirical g.f.: 35*x*(1 + 33*x - 32*x^2) / (1 - 2*x - 33*x^2 + 32*x^3). - Colin Barker, Jul 07 2018

cp's OEIS Frontend

A208836 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A208838 Number of nX6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A208835 Number of n X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A208837 Number of nX5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A208839 Number of nX7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A208841 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A208842 Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A208843 Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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A208844 Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

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