A183738 -id:A183738 - cp's OEIS frontend

A183731 1/16 the number of (n+1) X 3 0..7 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.

21, 290, 13169, 550268, 19849923, 667017027, 21320890377, 659741463420, 19939380387212, 592112324464323, 17343862233069362, 502495529472928971, 14428841233622907321, 411240107421964502725, 11647315145815312830954

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 2 of A183738.

			Some solutions with the first block increasing clockwise for 3 X 3:
..7..0..6....6..7..0....3..5..4....6..1..7....0..2..0....0..1..2....0..2..7
..4..1..4....4..2..1....2..7..3....5..2..5....7..3..7....6..4..3....7..3..6
..3..2..3....6..7..0....1..0..1....4..3..4....6..4..5....7..1..2....5..4..5
...
...R..L.......R..R.......R..L.......R..L.......R..L.......R..R.......R..L...
...R..L.......L..L.......R..L.......R..L.......R..L.......L..L.......R..L...

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

Empirical: a(n)=59*a(n-1)-983*a(n-2)+1517*a(n-3)+56964*a(n-4)-301681*a(n-5)-391561*a(n-6)+6287597*a(n-7)-12340851*a(n-8)-17981853*a(n-9)+86923852*a(n-10)-42259832*a(n-11)-195169753*a(n-12)+251286677*a(n-13)+147371126*a(n-14)-407605405*a(n-15)+42991424*a(n-16)+309052737*a(n-17)-122546216*a(n-18)-125908592*a(n-19)+73571657*a(n-20)+29253790*a(n-21)-21987805*a(n-22)-3922294*a(n-23)+3666493*a(n-24)+284823*a(n-25)-339999*a(n-26)-7395*a(n-27)+16089*a(n-28)-300*a(n-29)-300*a(n-30)+16*a(n-31).

A183730 1/16 the number of (n+1) X 2 0..7 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, 21, 563, 9403, 135578, 1814815, 23204876, 287769879, 3491293862, 41667398364, 490998416023, 5727556631915, 66266101711488, 761498455531330, 8701271226331052, 98948856313647335, 1120614615517688964

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 1 of A183738.

			Some solutions with the first block increasing clockwise for 3 X 2:
..4..5....6..0....1..2....1..2....2..4....4..5....7..0....2..3....0..2....0..2
..2..6....5..1....7..4....0..3....0..5....1..6....6..1....1..4....7..3....6..3
..1..7....4..2....6..5....7..4....7..6....0..7....4..3....0..7....6..4....5..4
...
...R.......R.......R.......R.......R.......R.......R.......R.......R.......R...
...R.......R.......R.......R.......R.......R.......R.......R.......R.......R...

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

Empirical: a(n)=18*a(n-1)-46*a(n-2)-342*a(n-3)-33*a(n-4)+435*a(n-5)-157*a(n-6)-37*a(n-7)+21*a(n-8)-2*a(n-9).

A183732 1/16 the number of (n+1) X 4 0..7 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

563, 13169, 469254, 32555965, 2610816897, 211915469907, 16635894447271, 1270931982853879, 94993985142144635, 6981985010723242050, 506415863251104840544, 36341705193868254651896, 2585229289237578869949797

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 3 of A183738.

			Some solutions with the first block increasing clockwise for 3 X 4:
..3..6..4..3....4..5..4..3....5..1..7..6....2..4..6..4....5..1..0..7
..1..0..1..2....0..7..0..1....3..2..3..4....1..0..7..0....4..3..4..5
..5..7..6..3....5..6..4..3....6..1..7..5....4..5..6..4....5..2..0..7
...
...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

A183733 1/16 the number of (n+1) X 5 0..7 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

9403, 550268, 32555965, 3202350892, 470757143497, 85938883577009, 16327766532728500, 3094892136980310870, 579019469263278106043, 106955380615838654906545, 19539849220501390068072761

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 4 of A183738.

			Some solutions with the first block increasing clockwise for 3 X 5:
..0..1..2..0..2....0..3..2..3..4....4..6..0..3..7....4..6..2..3..4
..7..4..3..6..5....7..6..0..6..5....3..2..1..2..1....3..0..1..7..6
..6..5..1..0..2....3..5..2..3..4....4..5..7..4..5....4..6..2..3..5
...
...R..R..L..R.......R..L..R..R.......R..R..L..R.......R..L..R..R...
...R..L..R..L.......L..R..L..L.......L..L..R..L.......L..R..L..L...

R. H. Hardin, Table of n, a(n) for n = 1..58

A183734 1/16 the number of (n+1) X 6 0..7 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

135578, 19849923, 2610816897, 470757143497, 121627738709359, 45102927396897679, 19628509753968319015, 8974005118250282637773, 4133062481661217572719434

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 5 of A183738.

			Some solutions with the first block increasing clockwise for 3 X 6:
..0..1..0..6..7..6....0..1..0..7..0..6....0..1..0..7..1..5....0..1..0..7..1..6
..3..2..3..5..0..1....3..2..4..5..3..5....3..2..4..5..2..3....3..2..4..6..2..3
..4..1..0..6..7..3....0..1..0..7..0..7....4..1..0..7..1..5....0..1..0..7..1..6
...
...R..L..L..R..L.......R..L..L..R..L.......R..L..L..R..L.......R..L..L..R..L...
...L..R..R..L..R.......L..R..R..L..R.......L..R..R..L..R.......L..R..R..L..R...

Cf. A183738.

A183735 1/16 the number of (n+1) X 7 0..7 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

1814815, 667017027, 211915469907, 85938883577009, 45102927396897679

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 6 of A183738.

			Some solutions with the first block increasing clockwise for 3 X 7:
..0..1..0..5..0..7..1....0..1..0..6..0..7..1....0..1..0..5..0..5..0
..3..2..3..4..3..5..4....3..2..3..4..2..5..3....3..2..3..4..1..3..2
..0..1..0..5..7..6..3....0..1..0..5..1..6..2....0..1..0..6..0..6..1
...
...R..L..L..R..L..R.......R..L..L..R..L..R.......R..L..L..R..L..R...
...L..R..R..L..R..L.......L..R..R..L..R..L.......L..R..R..L..R..L...

A183736 1/16 the number of (n+1) X 8 0..7 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

23204876, 21320890377, 16635894447271, 16327766532728500, 19628509753968319015

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 7 of A183738.

			Some solutions with the first block increasing clockwise for 3 X 8:
..0..1..0..1..7..5..2..0....0..1..0..1..0..1..0..7....0..1..0..1..5..0..1..5
..3..2..3..2..3..4..3..5....3..2..3..2..5..4..5..6....3..2..3..2..4..3..2..4
..0..1..0..1..0..6..7..6....0..1..0..1..7..3..2..0....0..1..0..1..7..0..1..5
...
...R..L..R..L..L..R..L.......R..L..R..L..R..L..L.......R..L..R..L..R..R..L...
...L..R..L..R..R..L..R.......L..R..L..R..L..R..R.......L..R..L..R..L..L..R...

A183737 1/16 the number of (n+1) X 9 0..7 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

287769879, 659741463420, 1270931982853879, 3094892136980310870, 8974005118250282637773

Offset: 1

R. H. Hardin, Jan 06 2011

nonn

Column 8 of A183738.

			Some solutions with the first block increasing clockwise for 3 X 9:
..0..1..0..1..0..6..1..6..7....0..1..0..1..0..7..0..6..7
..3..2..3..2..4..5..3..4..2....3..2..3..2..4..5..2..3..1
..0..1..0..1..0..6..1..5..0....0..1..0..1..0..6..7..4..7
...
...R..L..R..L..L..R..L..R.......R..L..R..L..L..R..L..R...
...L..R..L..R..R..L..R..L.......L..R..L..R..R..L..R..L...

cp's OEIS Frontend

A183731 1/16 the number of (n+1) X 3 0..7 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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A183730 1/16 the number of (n+1) X 2 0..7 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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A183732 1/16 the number of (n+1) X 4 0..7 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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A183733 1/16 the number of (n+1) X 5 0..7 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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A183734 1/16 the number of (n+1) X 6 0..7 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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A183735 1/16 the number of (n+1) X 7 0..7 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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A183736 1/16 the number of (n+1) X 8 0..7 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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A183737 1/16 the number of (n+1) X 9 0..7 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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