A233026 -id:A233026 - cp's OEIS frontend

A233020 Number of n X 2 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

3, 15, 81, 435, 2337, 12555, 67449, 362355, 1946673, 10458075, 56183721, 301834755, 1621541217, 8711375595, 46799960409, 251422553235, 1350712686993, 7256408541435, 38983468081161, 209430157488675, 1125117723605697

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

			Some solutions for n=5:
..0..2....0..0....0..0....0..1....0..0....0..0....0..1....0..2....0..0....0..0
..2..2....1..1....2..2....1..1....1..1....0..2....0..1....2..0....1..1....0..0
..3..2....1..1....2..3....0..0....0..0....2..2....0..1....2..0....1..1....1..1
..3..2....1..3....3..3....2..2....1..1....2..3....0..1....0..2....3..3....3..1
..2..3....3..3....3..2....0..0....3..1....2..3....0..1....0..2....2..3....3..1

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

Column 2 of A233026.

Empirical: a(n) = 5*a(n-1) + 2*a(n-2).
Conjectures from Colin Barker, Oct 06 2018: (Start)
G.f.: 3*x / (1 - 5*x - 2*x^2).
a(n) = sqrt(3/11)*(((5+sqrt(33))/2)^n - ((5-sqrt(33))/2)^n) = 3*A015535(n).
(End)

A233019 Number of n X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

1, 15, 849, 179999, 149128385, 487651369463, 6338787392715565, 328918675019714663095, 68332288847776936953486283, 56955693489584720827393016043135

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Diagonal of A233026

			Some solutions for n=4
..0..0..2..3....0..0..2..3....0..0..2..2....0..2..2..0....0..2..0..0
..0..2..2..2....2..0..2..2....2..0..0..2....0..2..0..2....2..0..2..2
..0..2..3..3....2..2..0..2....0..0..0..0....0..2..2..2....0..2..0..2
..0..2..2..3....0..0..2..2....0..0..0..0....0..2..0..2....2..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..11

A233021 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

9, 81, 849, 8835, 92067, 959385, 9997413, 104179551, 1085618895, 11312857317, 117887355777, 1228463178219, 12801387988827, 133398816787089, 1390102724464989, 14485777543658775, 150951255149241255

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

			Some solutions for n=5:
..0..1..0....0..0..1....0..0..0....0..1..0....0..1..3....0..0..0....0..1..0
..0..1..1....1..1..1....2..2..2....1..1..0....0..1..1....0..2..0....0..1..1
..0..1..0....3..3..3....3..2..0....1..0..0....1..1..1....2..0..2....1..1..1
..1..1..1....1..1..1....3..2..2....0..0..0....1..3..3....2..0..2....1..3..3
..1..0..0....3..3..1....2..2..2....0..0..2....1..1..1....2..2..2....3..3..2

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

Column 3 of A233026.

Empirical: a(n) = 11*a(n-1) - 5*a(n-2) - 11*a(n-3) + 2*a(n-4).

Empirical g.f.: 3*x*(3 - 6*x + x^2) / (1 - 11*x + 5*x^2 + 11*x^3 - 2*x^4). - Colin Barker, Oct 07 2018

A233022 Number of nX4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

27, 435, 8835, 179999, 3685017, 75489671, 1546718177, 31692006853, 649369155341, 13305594622397, 272632154901327, 5586243967145293, 114462368539181387, 2345338645585949507, 48056085480976430831, 984671171688465647531

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 4 of A233026

			Some solutions for n=4
..0..2..2..2....0..0..2..2....0..2..0..0....0..0..1..3....0..0..0..2
..0..2..2..2....2..2..2..2....2..0..2..0....0..0..1..1....2..2..2..0
..0..0..0..2....0..2..2..0....0..2..0..2....1..0..1..1....3..2..2..0
..1..0..2..2....2..2..2..0....2..0..0..0....1..0..0..1....3..2..2..0

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

Empirical: a(n) = 23*a(n-1) -39*a(n-2) -265*a(n-3) +180*a(n-4) +655*a(n-5) -156*a(n-6) -127*a(n-7) +20*a(n-8)

Empirical: G.f.: -x*(27-186*x-117*x^2+914*x^3+20*x^4-469*x^5+129*x^6)/(-1+23*x-39*x^2-265*x^3+180*x^4+655*x^5-156*x^6-127*x^7+20*x^8) . - R. J. Mathar, May 11 2022

A233023 Number of nX5 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

81, 2337, 92067, 3685017, 149128385, 6050598339, 245698677999, 9979662714381, 405380056659145, 16467175046293207, 668927350000203943, 27173135930635192613, 1103826618460521163805, 44839633474092471048067

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 5 of A233026

			Some solutions for n=3
..0..2..0..1..0....0..1..3..3..3....0..1..0..1..1....0..0..1..3..3
..0..0..0..0..1....1..1..3..1..1....0..1..0..1..1....1..1..1..1..3
..0..0..0..1..1....3..3..3..1..3....0..1..1..1..1....1..1..1..3..3

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

Empirical: a(n) = 59*a(n-1) -780*a(n-2) +619*a(n-3) +32493*a(n-4) -90013*a(n-5) -408784*a(n-6) +1361086*a(n-7) +1750387*a(n-8) -6258928*a(n-9) -3161760*a(n-10) +10671769*a(n-11) +1911277*a(n-12) -7549998*a(n-13) +65894*a(n-14) +2257616*a(n-15) -323424*a(n-16) -231416*a(n-17) +54784*a(n-18) +784*a(n-19) -480*a(n-20)

A233024 Number of nX6 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

243, 12555, 959385, 75489671, 6050598339, 487651369463, 39386531523609, 3183658674622011, 257414773440925415, 20815582600558673815, 1683301058522200223439, 136126239210040751513149

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 6 of A233026

			Some solutions for n=2
..0..0..2..3..3..3....0..2..2..3..2..0....0..1..0..1..0..0....0..0..1..1..1..1
..0..0..2..3..2..3....2..0..2..3..2..2....1..0..1..1..1..1....0..0..1..3..1..3

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 50

Empirical recurrence of order 50 (see link above)

A233025 Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

729, 67449, 9997413, 1546718177, 245698677999, 39386531523609, 6338787392715565, 1021854400935817069, 164848602838755709211, 26602184763154679609107, 4293469218556492461639273

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 7 of A233026

			Some solutions for n=2
..0..1..0..1..1..0..1....0..0..1..3..3..3..2....0..2..2..0..0..1..0
..1..0..0..1..0..1..1....1..0..1..3..2..2..3....2..2..2..0..1..0..1

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

cp's OEIS Frontend

A233020 Number of n X 2 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

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A233019 Number of n X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

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A233021 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

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A233022 Number of nX4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

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A233023 Number of nX5 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

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A233024 Number of nX6 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

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A233025 Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

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