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.

Showing 1-10 of 15 results. Next

A207442 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 14, 81, 108, 81, 14, 21, 196, 323, 333, 196, 22, 31, 441, 1058, 1360, 1144, 484, 35, 46, 961, 3223, 6092, 6525, 4048, 1225, 56, 68, 2116, 9515, 25689, 41092, 32393, 14743, 3136, 90, 100, 4624, 28426, 105690, 243981, 287176
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Table starts
..2....4.....6......9.......14........21.........31..........46............68
..4...16....36.....81......196.......441........961........2116..........4624
..6...36...108....323.....1058......3223.......9515.......28426.........84486
..9...81...333...1360.....6092.....25689.....105690......439332.......1821924
.14..196..1144...6525....41092....243981....1414091.....8282682......48412066
.22..484..4048..32393...287176...2405923...19685415...162644898....1341574108
.35.1225.14743.165626..2078416..24609889..284247216..3316383098...38630942068
.56.3136.54250.855471.15205846.254583643.4151434555.68394049216.1125157869978

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is Column 1 squared
Row 1 is A038718(n+2)
Row 2 is A207069

A207242 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 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, 18, 169, 283, 287, 196, 21, 25, 324, 699, 987, 882, 441, 31, 34, 625, 1526, 2884, 3866, 2491, 961, 46, 46, 1156, 3355, 7165, 13876, 13494, 6759, 2116, 68, 62, 2116, 6888, 17929, 40838, 58026, 44730, 18528
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Table starts
..2....4.....6......9.....13......18.......25.......34........46........62
..4...16....36.....81....169.....324......625.....1156......2116......3844
..6...36...102....283....699....1526.....3355.....6888.....13954.....27816
..9...81...287....987...2884....7165....17929....40646.....90602....196548
.14..196...882...3866..13876...40838...122197...323039....839664...2118081
.21..441..2491..13494..58026..197256...683257..2037721...5952936..16732138
.31..961..6759..44730.228110..886959..3510185.11662500..37779767.116530737
.46.2116.18528.150608.919413.4132837.18982182.71594896.262849612.914523558

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Row 1 is A171861(n+1)
Row 2 is A207025

A207269 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 82, 81, 14, 18, 169, 217, 193, 196, 21, 25, 324, 499, 611, 488, 441, 31, 34, 625, 1014, 1602, 1910, 1087, 961, 46, 46, 1156, 2141, 3513, 5904, 5132, 2305, 2116, 68, 62, 2116, 4188, 8327, 14184, 18055, 13067, 4932, 4624, 100, 83
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Table starts
..2....4....6.....9.....13.....18......25......34.......46.......62.......83
..4...16...36....81....169....324.....625....1156.....2116.....3844.....6889
..6...36...82...217....499...1014....2141....4188.....8150....15670....29517
..9...81..193...611...1602...3513....8327...17568....36988....76723...153865
.14..196..488..1910...5904..14184...38911...90670...211626...485438..1060958
.21..441.1087..5132..18055..45520..140295..349415...877101..2164569..5025447
.31..961.2305.13067..52240.135686..467686.1233127..3284096..8655283.21076355
.46.2116.4932.33937.156473.417772.1623957.4556171.12881467.36421182.93059536

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Row 1 is A171861(n+1)
Row 2 is A207025

A207426 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 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, 15, 81, 114, 81, 14, 25, 225, 361, 351, 196, 21, 40, 625, 1425, 1521, 1162, 441, 31, 64, 1600, 5625, 8463, 6889, 3633, 961, 46, 104, 4096, 20550, 47089, 55361, 29929, 11067, 2116, 68, 169, 10816, 75076, 241087, 444889, 341329
Offset: 1

Views

Author

R. H. Hardin Feb 17 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...114....361.....1425......5625......20550........75076........282494
..9...81...351...1521.....8463.....47089.....241087......1234321.......6520459
.14..196..1162...6889....55361....444889....3210938.....23174596.....174570082
.21..441..3633..29929...341329...3892729...39698733....404854641....4315250265
.31..961.11067.127449..2048823..32936121..474552171...6837470721..102807481767
.46.2116.33994.546121.12436631.283215241.5755114104.116947584576.2485504480392

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)

A207729 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 15, 81, 78, 81, 14, 25, 225, 169, 189, 196, 21, 40, 625, 611, 441, 490, 441, 31, 64, 1600, 2209, 2163, 1225, 1113, 961, 46, 104, 4096, 6016, 10609, 8575, 2809, 2449, 2116, 68, 169, 10816, 16384, 33063, 60025, 27931, 6241, 5474, 4624
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2....4....6.....9.....15......25.......40.......64........104.........169
..4...16...36....81....225.....625.....1600.....4096......10816.......28561
..6...36...78...169....611....2209.....6016....16384......51840......164025
..9...81..189...441...2163...10609....33063...103041.....418263.....1697809
.14..196..490..1225...8575...60025...211680...746496....4078944....22287841
.21..441.1113..2809..27931..277729..1029231..3814209...27996255...205492225
.31..961.2449..6241..88243.1247689..4799749.18464209..184732327..1848226081
.46.2116.5474.14161.288813.5890329.23473944.93547584.1307760792.18282014521

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)

A207123 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 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, 14, 81, 102, 81, 12, 21, 196, 288, 289, 144, 16, 31, 441, 896, 1024, 612, 256, 20, 46, 961, 2499, 4096, 2560, 1296, 400, 25, 68, 2116, 6634, 14161, 12288, 6400, 2340, 625, 30, 100, 4624, 17848, 45796, 49861, 36864, 13200, 4225, 900
Offset: 1

Views

Author

R. H. Hardin Feb 15 2012

Keywords

Comments

Table starts
..2...4....6.....9.....14......21......31.......46........68........100
..4..16...36....81....196.....441.....961.....2116......4624......10000
..6..36..102...288....896....2499....6634....17848.....47192.....122200
..9..81..289..1024...4096...14161...45796...150544....481636....1493284
.12.144..612..2560..12288...49861..186822...712756...2628872....9322638
.16.256.1296..6400..36864..175561..762129..3374569..14348944...58201641
.20.400.2340.13200..87744..475984.2330037.11635558..55554808..251535759
.25.625.4225.27225.208849.1290496.7123561.40119556.215091556.1087086841

Examples

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

Links

Crossrefs

Column 1 is A002620(n+2)
Column 2 is A030179(n+2)
Row 1 is A038718(n+2)
Row 2 is A207069
Row 3 is A207070

A207564 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 14, 81, 92, 81, 14, 21, 196, 241, 221, 196, 22, 31, 441, 720, 636, 618, 484, 35, 46, 961, 1889, 2234, 2135, 1690, 1225, 56, 68, 2116, 4719, 6315, 9568, 6709, 4861, 3136, 90, 100, 4624, 12102, 16812, 32823, 36426, 23276, 13900
Offset: 1

Views

Author

R. H. Hardin Feb 18 2012

Keywords

Comments

Table starts
..2....4.....6.....9.....14......21.......31........46........68........100
..4...16....36....81....196.....441......961......2116......4624......10000
..6...36....92...241....720....1889.....4719.....12102.....30414......74588
..9...81...221...636...2234....6315....16812.....47596....129150.....337186
.14..196...618..2135...9568...32823...106833....378104...1270366....4115246
.22..484..1690..6709..36426..138017...493471...1980774...7259428...25276248
.35.1225..4861.23276.160652..738515..3275898..16648464..77299468..346860730
.56.3136.13900.78733.666212.3451393.17232331.100565794.513390118.2498101416

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A038718(n+2)
Row 2 is A207069
Row 3 is A207414

A207762 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 82, 81, 14, 19, 169, 221, 193, 196, 21, 28, 361, 493, 663, 488, 441, 31, 41, 784, 1095, 1664, 2245, 1087, 961, 46, 60, 1681, 2654, 4018, 6552, 6459, 2305, 2116, 68, 88, 3600, 6203, 11509, 16920, 21547, 17563, 4932, 4624, 100
Offset: 1

Views

Author

R. H. Hardin Feb 19 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...82...221....493...1095....2654.....6203....14182.....33242
..9...81..193...663...1664...4018...11509....30943....79178....213444
.14..196..488..2245...6552..16920...59252...188350...538950...1709438
.21..441.1087..6459..21547..56651..235872...862146..2629798...9529570
.31..961.2305.17563..67330.178627..887114..3733566.11979209..49800326
.46.2116.4932.48649.217902.581166.3488718.17141340.57575203.278302021

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Column 3 is A207264
Row 1 is A000930(n+3)
Row 2 is A207170

A208688 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 78, 81, 14, 26, 256, 282, 189, 196, 21, 42, 676, 768, 927, 490, 441, 31, 68, 1764, 2430, 2889, 3430, 1113, 961, 46, 110, 4624, 7086, 11727, 12096, 11067, 2449, 2116, 68, 178, 12100, 21588, 40581, 66094, 41013, 34627
Offset: 1

Views

Author

R. H. Hardin Mar 01 2012

Keywords

Comments

Table starts
..2....4....6.....10.....16......26.......42........68........110.........178
..4...16...36....100....256.....676.....1764......4624......12100.......31684
..6...36...78....282....768....2430.....7086.....21588......64230......193554
..9...81..189....927...2889...11727....40581....154359.....554733.....2062215
.14..196..490...3430..12096...66094...269766...1331988....5795314....27403166
.21..441.1113..11067..41013..301035..1346961...8556723...42184905...249260739
.31..961.2449..34627.133207.1332721..6398617..53340739..290904031..2188890625
.46.2116.5474.111642.444912.6219706.31733422.358035204.2130519946.21086588370

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Column 3 is A207724
Row 1 is A006355(n+2)
Row 2 is A206981

Formula

Empirical for row n:
n=1: a(k)=a(k-1)+a(k-2)
n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3)
n=3: a(k)=2*a(k-1)+4*a(k-2)-3*a(k-3)
n=4: a(k)=a(k-1)+10*a(k-2)+2*a(k-3)-10*a(k-4)
n=5: a(k)=a(k-1)+17*a(k-2)+4*a(k-3)-32*a(k-4)
n=6: a(k)=a(k-1)+26*a(k-2)+6*a(k-3)-78*a(k-4)
n=7: a(k)=a(k-1)+39*a(k-2)+9*a(k-3)-180*a(k-4)

A207391 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 14, 81, 98, 64, 10, 21, 196, 271, 200, 100, 12, 31, 441, 834, 643, 350, 144, 14, 46, 961, 2307, 2356, 1271, 556, 196, 16, 68, 2116, 6115, 7561, 5348, 2239, 826, 256, 18, 100, 4624, 16544, 23071, 19319, 10570, 3641, 1168, 324, 20, 147
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Table starts
..2...4....6....9....14.....21.....31......46.......68......100.......147
..4..16...36...81...196....441....961....2116.....4624....10000.....21609
..6..36...98..271...834...2307...6115...16544....44250...116526....307117
..8..64..200..643..2356...7561..23071...72410...223804...678174...2060069
.10.100..350.1271..5348..19319..65955..232892...806886..2731598...9282799
.12.144..556.2239.10570..42167.158217..616386..2348280..8718366..32527713
.14.196..826.3641.18972..82477.335915.1424240..5887228.23664574..95673277
.16.256.1168.5581.31710.148743.651531.2975974.13215696.56972122.247183399

Examples

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

Links

Crossrefs

Column 1 is A004275(n+1)
Column 2 is A016742
Column 3 is A207106
Column 4 is A207107
Row 1 is A038718(n+2)
Row 2 is A207069

Formula

Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n
k=4: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1
k=5: a(n) = (2/15)*n^5 + (55/12)*n^4 + (101/6)*n^3 + (5/12)*n^2 - (299/30)*n + 2
k=6: a(n) = (1/36)*n^6 + (113/60)*n^5 + (151/9)*n^4 + (95/4)*n^3 - (605/36)*n^2 - (229/30)*n + 3
k=7: a(n) = (1/210)*n^7 + (103/180)*n^6 + (197/20)*n^5 + (1439/36)*n^4 + (293/20)*n^3 - (3469/90)*n^2 + (157/105)*n + 3
Showing 1-10 of 15 results. Next

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

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