A183729 -id:A183729 - cp's OEIS frontend

A183727 1/12 the number of (n+1) X 8 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

16731, 388998, 8439116, 200260149, 4858574535, 134020420595, 5585215240568, 460509744129719, 54842127230404464, 7095042727449540024, 920742012786042810982, 118354309394343482912431

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 7 of A183729.

			Some solutions with the first block increasing clockwise for 3 X 8:
..1..2..1..3..2..1..3..2....1..2..1..0..2..1..2..1....1..2..1..2..1..2..1..0
..0..5..0..4..5..0..4..0....0..3..4..5..4..5..4..0....0..4..5..4..5..3..4..5
..1..3..2..3..2..1..3..1....1..2..1..0..3..2..3..2....2..3..1..3..1..2..1..0
...
...R..L..R..L..L..R..L.......R..L..L..R..L..R..L.......R..L..R..L..R..L..L...
...L..R..L..R..R..L..R.......L..R..R..L..R..L..R.......L..R..L..R..L..R..R...

R. H. Hardin, Table of n, a(n) for n = 1..18

A183721 1/12 the number of (n+1) X 2 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

Original entry on oeis.org

0, 1, 12, 87, 537, 3070, 16731, 88331, 455804, 2311983, 11571209, 57295330, 281223411, 1370286715, 6635743136, 31964799247, 153273890393, 732031932806, 3483896304443, 16529018119643, 78202676604548, 369073777749215

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 1 of A183729.

			All solutions with the first block increasing clockwise for 3 X 2:
..3..4....1..2....4..5....2..3....5..0....0..1
..2..5....0..3....3..0....1..4....4..1....5..2
..1..0....5..4....2..1....0..5....3..2....4..3
...
...R.......R.......R.......R.......R.......R...
...R.......R.......R.......R.......R.......R...

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A183729.

Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 23*a(n-3) + 6*a(n-4) + 7*a(n-5) - 2*a(n-6).

Empirical g.f.: x^2*(1 + 2*x - x^2)^2 / ((1 + x)*(1 - 5*x + 2*x^2)*(1 - 4*x - 2*x^2 + x^3)). - Colin Barker, Apr 04 2018

A183722 1/12 the number of (n+1) X 3 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

Original entry on oeis.org

1, 2, 29, 388, 4170, 41423, 388998, 3528126, 31206553, 270945278, 2318825000, 19619049541, 164448364546, 1367755750914, 11301610770163, 92861669073522, 759320826126174, 6182626278886591, 50153160109476104, 405492870969390486

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 2 of A183729.

			Some solutions with the first block increasing clockwise for 5 X 3:
..2..4..3....4..0..3....1..4..2....1..2..1....1..2..1....1..3..2....3..5..4
..1..0..1....2..1..2....0..5..0....0..5..0....0..3..0....5..4..5....2..1..2
..2..5..2....3..0..3....1..4..1....1..4..1....5..4..5....0..3..0....3..0..3
..3..4..3....4..5..4....2..3..2....2..3..2....0..2..0....1..2..1....4..5..4
..1..5..1....1..0..2....0..4..0....5..4..1....5..3..4....4..3..5....2..1..2
...
...R..L.......R..L.......R..L.......R..L.......R..L.......R..L.......R..L...
...L..R.......L..R.......L..R.......L..R.......R..L.......L..R.......L..R...
...L..R.......L..R.......L..R.......L..R.......L..R.......L..R.......L..R...
...R..L.......R..L.......R..L.......R..L.......R..L.......R..L.......R..L...

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=14*a(n-1)-36*a(n-2)-115*a(n-3)+125*a(n-4)+164*a(n-5)-155*a(n-6)-29*a(n-7)+34*a(n-8)+a(n-9)-2*a(n-10).

A183723 1/12 the number of (n+1) X 4 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

Original entry on oeis.org

12, 29, 124, 1790, 30939, 525895, 8439116, 130610844, 1967828529, 29070445544, 422988995515, 6081228134954, 86580348551185, 1222760452357981, 17151917685428842, 239202719875959959, 3319294757106439138

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 3 of A183729.

			Some solutions with the first block increasing clockwise for 3 X 4:
..4..5..4..3....1..2..1..0....3..5..4..3....4..5..0..5....0..1..0..5
..1..0..1..2....0..3..4..5....1..0..1..2....3..2..1..2....3..2..3..4
..4..5..4..3....1..2..1..0....3..5..4..3....4..5..0..4....4..1..0..5
...
...R..L..L.......R..L..L.......R..L..L.......R..R..L.......R..L..L...
...L..R..R.......L..R..R.......L..R..R.......L..L..R.......L..R..R...

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=22*a(n-1)-8*a(n-2)-2038*a(n-3)+4849*a(n-4)+60267*a(n-5)-204061*a(n-6)-712337*a(n-7)+3325947*a(n-8)+3154325*a(n-9)-27076488*a(n-10)+4020761*a(n-11)+122413547*a(n-12)-93348742*a(n-13)-325835425*a(n-14)+402806197*a(n-15)+514609889*a(n-16)-925150963*a(n-17)-439511369*a(n-18)+1310144478*a(n-19)+86470889*a(n-20)-1199641648*a(n-21)+219926386*a(n-22)+717789749*a(n-23)-257447414*a(n-24)-276848427*a(n-25)+139910715*a(n-26)+66195171*a(n-27)-44059046*a(n-28)-8998172*a(n-29)+8348721*a(n-30)+522019*a(n-31)-936761*a(n-32)+15437*a(n-33)+58686*a(n-34)-3505*a(n-35)-1816*a(n-36)+147*a(n-37)+21*a(n-38)-2*a(n-39).

A183724 1/12 the number of (n+1) X 5 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

Original entry on oeis.org

87, 388, 1790, 14886, 272215, 7319684, 200260149, 5355252106, 139489865583, 3561214845505, 89499710973670, 2221523267475056, 54589402697720455, 1330321340313497085, 32193928583886647023, 774480659129262018036

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 4 of A183729.

			Some solutions with the first block increasing clockwise for 3 X 5:
..0..1..2..1..2....2..4..3..2..4....0..1..2..1..2....5..0..4..5..0
..5..4..3..5..4....1..5..0..1..0....5..4..3..5..3....2..1..3..2..1
..0..1..2..1..2....2..4..3..2..3....0..1..2..0..2....3..0..4..5..0
...
...R..R..L..R.......R..L..L..R.......R..R..L..R.......R..L..R..R...
...L..L..R..L.......L..R..R..L.......L..L..R..L.......L..R..L..L...

R. H. Hardin, Table of n, a(n) for n = 1..200

A183725 1/12 the number of (n+1) X 6 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

Original entry on oeis.org

537, 4170, 30939, 272215, 3723606, 112949014, 4858574535, 221403152762, 9949950285008, 439077020908186, 19070687313534907, 817844594324788300, 34712759917922473170, 1460861248287305883035, 61042039866448977229798

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 5 of A183729.

			Some solutions with the first block increasing clockwise for 3 X 6:
..0..1..0..5..0..3....2..3..1..2..3..1....0..1..5..0..1..4....1..2..0..1..2..0
..3..2..3..4..1..2....0..5..0..5..4..5....4..3..4..3..2..3....4..3..5..4..3..5
..4..1..0..5..0..4....3..4..1..2..3..1....5..1..5..0..1..0....0..2..0..1..2..0
...
...R..L..L..R..L.......R..L..R..R..L.......R..L..R..R..L.......R..L..R..R..L...
...L..R..R..L..R.......L..R..L..L..R.......L..R..L..L..R.......L..R..L..L..R...

R. H. Hardin, Table of n, a(n) for n = 1..125

A183726 1/12 the number of (n+1) X 7 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

Original entry on oeis.org

3070, 41423, 525895, 7319684, 112949014, 2740758406, 134020420595, 9546147995730, 729082624201394, 55559473375122011, 4177316401273489526, 310180873007618124181, 22791464284740341972598, 1660173775969136404275224

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 6 of A183729.

			Some solutions with the first block increasing clockwise for 3 X 7:
..1..2..0..1..2..0..1....1..2..3..1..2..1..2....2..5..4..3..4..1..2
..4..3..5..4..3..5..4....0..5..4..0..4..0..4....1..0..1..2..5..0..5
..0..1..0..1..2..0..2....1..2..3..1..3..1..3....3..5..4..3..4..2..3
...
...R..L..R..R..L..R.......R..R..L..R..L..R.......R..L..L..R..L..R...
...L..R..L..L..R..L.......L..L..R..L..R..L.......L..R..R..L..R..L...

R. H. Hardin, Table of n, a(n) for n = 1..59

A183720 1/12 the number of (n+1) X (n+1) 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

Original entry on oeis.org

0, 2, 124, 14886, 3723606, 2740758406, 5585215240568, 33429749952933774, 583208471844467888006

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Diagonal of A183729.

			Some solutions with the first block increasing clockwise for 3 X 3:
..5..0..1....1..2..3....4..5..4....2..3..2....0..1..2....5..0..5....3..4..3
..4..3..2....0..5..4....3..0..3....1..4..1....5..4..3....4..1..4....2..5..2
..5..0..1....1..2..3....2..1..2....0..5..0....0..1..2....3..2..3....1..0..1
...
...R..R.......R..R.......R..L.......R..L.......R..R.......R..L.......R..L...
...L..L.......L..L.......R..L.......R..L.......L..L.......R..L.......R..L...

A183728 1/12 the number of (n+1) X 9 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

Original entry on oeis.org

88331, 3528126, 130610844, 5355252106, 221403152762, 9546147995730, 460509744129719, 33429749952933774, 4646656755908387234, 935845545638421963156

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 8 of A183729.

			Some solutions with the first block increasing clockwise for 3 X 9:
..1..2..1..0..1..5..2..5..1....1..2..1..0..1..0..1..4..5
..0..3..4..5..2..4..3..4..3....0..3..4..5..3..4..2..3..2
..1..2..1..0..1..5..2..1..2....1..2..1..0..1..5..1..5..1
...
...R..L..L..R..L..R..L..R.......R..L..L..R..L..R..L..R...
...L..R..R..L..R..L..R..L.......L..R..R..L..R..L..R..L...

Cf. A183729.

cp's OEIS Frontend

A183727 1/12 the number of (n+1) X 8 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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A183721 1/12 the number of (n+1) X 2 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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A183722 1/12 the number of (n+1) X 3 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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A183723 1/12 the number of (n+1) X 4 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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A183724 1/12 the number of (n+1) X 5 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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A183725 1/12 the number of (n+1) X 6 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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A183726 1/12 the number of (n+1) X 7 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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A183720 1/12 the number of (n+1) X (n+1) 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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A183728 1/12 the number of (n+1) X 9 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

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