cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-17 of 17 results.

A207918 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 10, 13, 81, 98, 100, 16, 19, 169, 271, 358, 256, 26, 28, 361, 665, 1309, 1152, 676, 42, 41, 784, 1675, 4181, 5371, 3910, 1764, 68, 60, 1681, 4344, 13759, 21145, 23637, 12994, 4624, 110, 88, 3600, 11081, 46800, 86255, 117835
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4.....6......9......13.......19........28.........41..........60
..4...16....36.....81.....169......361.......784.......1681........3600
..6...36....98....271.....665.....1675......4344......11081.......28136
.10..100...358...1309....4181....13759.....46800.....156135......518564
.16..256..1152...5371...21145....86255....366330....1520815.....6276388
.26..676..3910..23637..117835...612439...3327954...17621905....92785236
.42.1764.12994.101069..628945..4105063..28188778..187980955..1245595210
.68.4624.43596.438103.3426491.28280693.247024548.2088382007.17532981294

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207462
Row 1 is A000930(n+3)
Row 2 is A207170
Row 3 is A207306

A208013 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 90, 81, 12, 19, 169, 261, 225, 144, 16, 28, 361, 624, 841, 420, 256, 20, 41, 784, 1482, 2304, 1943, 784, 400, 25, 60, 1681, 3808, 6084, 5952, 4489, 1260, 625, 30, 88, 3600, 9512, 18496, 16224, 15376, 8643, 2025, 900, 36, 129
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Table starts
..2...4....6.....9....13.....19.....28......41.......60.......88.......129
..4..16...36....81...169....361....784....1681.....3600.....7744.....16641
..6..36...90...261...624...1482...3808....9512....23280....58080....144996
..9..81..225...841..2304...6084..18496...53824...150544...435600...1263376
.12.144..420..1943..5952..16224..55624..181192...545140..1737120...5591900
.16.256..784..4489.15376..43264.167281..609961..1974025..6927424..24750625
.20.400.1260..8643.32860..92560.393049.1578401..5340405.20121640..78251775
.25.625.2025.16641.70225.198025.923521.4084441.14447601.58446025.247401441

Examples

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

Links

Crossrefs

Column 1 is A002620(n+2)
Column 2 is A030179(n+2)
Column 3 is A207363
Row 1 is A000930(n+3)
Row 2 is A207170
Row 3 is A207171

A208039 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 15, 81, 102, 81, 13, 25, 225, 289, 279, 169, 19, 40, 625, 1071, 961, 741, 361, 28, 64, 1600, 3969, 4743, 3249, 1995, 784, 41, 104, 4096, 13230, 23409, 21147, 11025, 5404, 1681, 60, 169, 10816, 44100, 100215, 137641, 94605
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Table starts
..2....4.....6......9......15.......25........40.........64.........104
..4...16....36.....81.....225......625......1600.......4096.......10816
..6...36...102....289....1071.....3969.....13230......44100......153090
..9...81...279....961....4743....23409....100215.....429025.....1942075
.13..169...741...3249...21147...137641....766115....4264225....25232235
.19..361..1995..11025...94605...811801...5866411...42393121...327288437
.28..784..5404..37249..422477..4791721..44918280..421070400..4242161160
.41.1681.14555.126025.1889665.28334329.344414069.4186478209.55078752265

Examples

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

Links

Crossrefs

Column 1 is A000930(n+3)
Column 2 is A207170
Column 3 is A208023
Column 4 is A141583(n+3) for n>1
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)
Row 3 is A207704

A208164 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 102, 81, 14, 19, 169, 281, 287, 196, 21, 28, 361, 699, 981, 882, 441, 31, 41, 784, 1799, 2920, 3893, 2491, 961, 46, 60, 1681, 4706, 9039, 14446, 13825, 6759, 2116, 68, 88, 3600, 12161, 28681, 55576, 63031, 46611, 18528
Offset: 1

Views

Author

R. H. Hardin Feb 24 2012

Keywords

Comments

Table starts
..2....4.....6......9......13......19.......28........41.........60..........88
..4...16....36.....81.....169.....361......784......1681.......3600........7744
..6...36...102....281.....699....1799.....4706.....12161......31356.......81206
..9...81...287....981....2920....9039....28681.....89623.....278652......872602
.14..196...882...3893...14446...55576...222487....873641....3397748....13352522
.21..441..2491..13825...63031..297702..1474641...7151473...34264481...166182659
.31..961..6759..46611..258952.1493661..9072707..53874293..315713411..1874906825
.46.2116.18528.159545.1088966.7719181.57903614.424153857.3061342878.22414028568

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Column 3 is A207237
Row 1 is A000930(n+3)
Row 2 is A207170
Row 3 is A207961

A209224 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 15, 81, 60, 81, 13, 25, 225, 100, 126, 169, 19, 40, 625, 240, 196, 234, 361, 28, 64, 1600, 576, 504, 324, 456, 784, 41, 104, 4096, 1296, 1296, 900, 576, 896, 1681, 60, 169, 10816, 2916, 3312, 2500, 1776, 1024, 1722, 3600, 88, 273
Offset: 1

Views

Author

R. H. Hardin Mar 06 2012

Keywords

Comments

Table starts
..2....4....6....9...15....25....40.....64.....104.....169......273......441
..4...16...36...81..225...625..1600...4096...10816...28561....74529...194481
..6...36...60..100..240...576..1296...2916....6804...15876....36288....82944
..9...81..126..196..504..1296..3312...8464...21712...55696...142544...364816
.13..169..234..324..900..2500..6900..19044...52992..147456...407808..1127844
.19..361..456..576.1776..5476.15984..46656..143856..443556..1312020..3880900
.28..784..896.1024.3456.11664.38232.125316..423384.1430416..4755296.15808576
.41.1681.1722.1764.6300.22500.80400.287296.1037696.3748096.13540384.48916036

Examples

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

Links

Crossrefs

Column 1 is A000930(n+3)
Column 2 is A207170
Column 3 is A208496
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)
Row 3 is A207694

A231977 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

Original entry on oeis.org

9, 16, 16, 36, 56, 36, 81, 169, 169, 81, 169, 550, 841, 550, 169, 361, 1764, 4489, 4489, 1764, 361, 784, 5680, 24964, 43983, 24964, 5680, 784, 1681, 18225, 136900, 417316, 417316, 136900, 18225, 1681, 3600, 58596, 741321, 3844551, 6507601, 3844551
Offset: 1

Views

Author

R. H. Hardin, Nov 16 2013

Keywords

Comments

Table starts
....9.....16........36..........81...........169..............361
...16.....56.......169.........550..........1764.............5680
...36....169.......841........4489.........24964...........136900
...81....550......4489.......43983........417316..........3844551
..169...1764.....24964......417316.......6507601........100540729
..361...5680....136900.....3844551.....100540729.......2641967397
..784..18225....741321....35366809....1557328369......69043343121
.1681..58596...4024036...328433132...24225988609....1809552010404
.3600.188356..21911761..3052452001..376708702756...47496507516441
.7744.605458.119268241.28290095075.5849616285604.1245162776547248

Examples

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

Links

Crossrefs

Column 1 is A207170 for n>1

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)
k=2: a(n) = 3*a(n-1) +2*a(n-3) +4*a(n-4) -10*a(n-5) -2*a(n-6) -a(n-8) +a(n-9)
k=3: [order 21]
k=4: [order 49]

A207879 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 72, 81, 13, 19, 169, 164, 164, 169, 19, 28, 361, 336, 400, 336, 361, 28, 41, 784, 702, 824, 824, 702, 784, 41, 60, 1681, 1488, 1940, 1648, 1940, 1488, 1681, 60, 88, 3600, 3164, 4200, 4160, 4160, 4200, 3164, 3600, 88, 129
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4....6....9....13....19.....28.....41.....60......88.....129......189
..4...16...36...81...169...361....784...1681...3600....7744...16641....35721
..6...36...72..164...336...702...1488...3164...6612...13916...29532....62032
..9...81..164..400...824..1940...4200...9276..21004...46026..102674...228630
.13..169..336..824..1648..4160...8892..19710..44868..100056..224792...497348
.19..361..702.1940..4160.10742..24952..61530.143916..341856..844144..1976858
.28..784.1488.4200..8892.24952..51696.136490.313524..741944.1781472..4256398
.41.1681.3164.9276.19710.61530.136490.380632.932930.2455492.6227022.15894853

Examples

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

Links

Crossrefs

Column 1 is A000930(n+3)
Column 2 is A207170
Column 3 is A207683
Previous Showing 11-17 of 17 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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