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 18 results. Next

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)

A207693 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 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, 144, 169, 18, 40, 625, 240, 256, 312, 324, 25, 64, 1600, 576, 768, 576, 612, 625, 34, 104, 4096, 1296, 2304, 1872, 1156, 1250, 1156, 46, 169, 10816, 2916, 5856, 6084, 4216, 2500, 2516, 2116, 62, 273
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2....4....6....9....15.....25.....40......64.....104......169.......273
..4...16...36...81...225....625...1600....4096...10816....28561.....74529
..6...36...60..100...240....576...1296....2916....6804....15876.....36288
..9...81..144..256...768...2304...5856...14884...42700...122500....320600
.13..169..312..576..1872...6084..18564...56644..177548...556516...1724752
.18..324..612.1156..4216..15376..50096..163216..578528..2050624...6804864
.25..625.1250.2500.10000..40000.145200..527076.2056032..8020224..29854944
.34.1156.2516.5476.24420.108900.453420.1887876.8263236.36168196.155101060

Examples

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

Links

Crossrefs

Column 1 is A171861(n+1)
Column 2 is A207025
Column 3 is A207584
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)

A207908 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 0 1 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, 261, 169, 18, 40, 625, 1071, 841, 611, 324, 25, 64, 1600, 3969, 4089, 2209, 1278, 625, 34, 104, 4096, 13230, 19881, 13865, 5041, 2625, 1156, 46, 169, 10816, 44100, 80511, 87025, 39831, 11025
Offset: 1

Views

Author

R. H. Hardin Feb 21 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..102...289...1071....3969....13230.....44100.....153090......531441
..9...81..261...841...4089...19881....80511....326041....1428071.....6255001
.13..169..611..2209..13865...87025...417425...2002225...10896915....59305401
.18..324.1278..5041..39831..314721..1726758...9474084...62431074...411400089
.25..625.2625.11025.110775.1113025..6835345..41977441..336253621..2693506201
.34.1156.5134.22801.289467.3674889.24832818.167806116.1627138986.15777620881

Examples

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

Links

Crossrefs

Column 1 is A171861(n+1)
Column 2 is A207025
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)
Row 3 is A207704

A207928 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 10, 15, 81, 72, 100, 16, 25, 225, 144, 240, 256, 26, 40, 625, 360, 576, 704, 676, 42, 64, 1600, 900, 1872, 1936, 2080, 1764, 68, 104, 4096, 2160, 6084, 7744, 6400, 6216, 4624, 110, 169, 10816, 5184, 18096, 30976, 29760, 21904
Offset: 1

Views

Author

R. H. Hardin Feb 21 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....72...144....360.....900.....2160......5184.....12528......30276
.10..100...240...576...1872....6084....18096.....53824....165648.....509796
.16..256...704..1936...7744...30976...111584....401956...1513992....5702544
.26..676..2080..6400..29760..138384...592968...2540836..11151624...48944016
.42.1764..6216.21904.126688..732736..3773248..19430464.105642128..574369156
.68.4624.18496.73984.520608.3663396.22906752.143233024.955190016.6369955344

Examples

			Some solutions for n=9 k=3
..0..0..1....0..0..1....0..1..1....1..0..0....1..0..0....0..0..1....0..0..1
..0..1..1....1..1..1....0..0..1....1..0..0....0..0..1....1..1..1....0..0..1
..1..1..0....1..0..0....1..0..0....0..1..1....1..1..0....1..1..0....1..1..0
..1..0..0....0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..1..1
..0..1..1....1..1..0....1..1..1....1..1..0....0..0..1....1..0..1....1..0..0
..0..1..1....0..0..1....1..0..0....1..0..0....1..1..0....1..1..0....0..1..1
..1..0..0....1..0..0....0..1..1....0..1..1....0..1..1....0..1..1....1..0..1
..1..1..0....1..1..1....1..1..1....1..0..0....0..0..1....0..0..1....1..0..0
..0..1..1....0..1..1....1..0..0....1..1..1....1..0..0....1..1..0....0..1..1

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207840
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)

A208108 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 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, 15, 81, 78, 81, 14, 25, 225, 169, 171, 196, 22, 40, 625, 611, 361, 406, 484, 35, 64, 1600, 2209, 1805, 841, 990, 1225, 56, 104, 4096, 6016, 9025, 6235, 2025, 2485, 3136, 90, 169, 10816, 16384, 25555, 46225, 22995, 5041, 6328, 8100
Offset: 1

Views

Author

R. H. Hardin Feb 23 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..171...361...1805.....9025....25555....72361.....292941.....1185921
.14..196..406...841...6235....46225...134160...389376....2189616....12313081
.22..484..990..2025..22995...261121...768544..2262016...18608992...153091129
.35.1225.2485..5041..89815..1600225..4747545.14085009..176312187..2207026441
.56.3136.6328.12769.361261.10220809.30461016.90782784.1769397240.34486347025

Examples

			Some solutions for n=10 k=3
..1..0..0....0..0..1....1..0..1....1..1..0....1..0..0....0..1..1....0..0..1
..0..0..1....1..0..0....0..1..1....0..1..1....0..0..1....1..1..0....0..0..1
..1..0..0....0..1..1....0..0..1....1..1..0....1..1..0....0..1..1....1..0..1
..0..1..1....1..0..0....0..0..1....0..1..1....0..0..1....1..1..0....0..0..1
..1..0..0....0..1..1....0..1..1....1..1..0....1..0..0....0..1..1....1..0..1
..0..1..1....1..0..0....0..0..1....0..1..1....0..0..1....1..1..0....0..0..1
..1..0..0....0..0..1....1..1..1....1..1..0....1..0..0....0..1..1....1..1..1
..0..0..1....1..0..0....0..0..1....0..1..1....0..0..1....1..1..0....0..0..1
..1..1..0....0..1..1....1..1..1....1..1..0....1..0..0....0..1..1....0..0..1
..0..0..1....1..0..0....0..0..1....0..1..1....0..0..1....1..1..0....0..1..1

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)
Row 3 is A207730

A207599 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 15, 81, 90, 64, 10, 25, 225, 225, 168, 100, 12, 40, 625, 825, 441, 270, 144, 14, 64, 1600, 3025, 1995, 729, 396, 196, 16, 104, 4096, 9240, 9025, 3915, 1089, 546, 256, 18, 169, 10816, 28224, 30400, 21025, 6765, 1521, 720, 324, 20, 273
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2...4...6....9....15.....25.....40......64......104......169.......273
..4..16..36...81...225....625...1600....4096....10816....28561.....74529
..6..36..90..225...825...3025...9240...28224....93912...312481....997815
..8..64.168..441..1995...9025..30400..102400...403520..1590121...5746377
.10.100.270..729..3915..21025..75400..270400..1223560..5536609..21791133
.12.144.396.1089..6765..42025.157440..589824..3005184.15311569..64177113
.14.196.546.1521.10725..75625.292600.1132096..6404216.36228361.159389139
.16.256.720.2025.15975.126025.499840.1982464.12318592.76545001.350003745

Examples

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

Links

Crossrefs

Column 2 is A016742.
Column 3 is A152746.
Column 4 is A016946(n-1).
Row 1 is A006498(n+2).
Row 2 is A189145(n+2).

Formula

Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = 12*n^2 - 6*n
k=4: a(n) = 36*n^2 - 36*n + 9
k=5: a(n) = 30*n^3 + 15*n^2 - 45*n + 15
k=6: a(n) = 25*n^4 + 50*n^3 - 25*n^2 - 50*n + 25
k=7: a(n) = 120*n^4 + 40*n^3 - 200*n^2 + 80*n

A207703 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 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, 15, 81, 102, 64, 10, 25, 225, 289, 216, 100, 12, 40, 625, 1071, 729, 390, 144, 14, 64, 1600, 3969, 3321, 1521, 636, 196, 16, 104, 4096, 13230, 15129, 8151, 2809, 966, 256, 18, 169, 10816, 44100, 61254, 43681, 17225, 4761, 1392
Offset: 1

Views

Author

R. H. Hardin, Feb 19 2012

Keywords

Comments

Table starts
..2...4....6....9....15.....25......40.......64.......104.......169........273
..4..16...36...81...225....625....1600.....4096.....10816.....28561......74529
..6..36..102..289..1071...3969...13230....44100....153090....531441....1815939
..8..64..216..729..3321..15129...61254...248004...1050282...4447881...18510693
.10.100..390.1521..8151..43681..206910...980100...4863870..24137569..117661437
.12.144..636.2809.17225.105625..571350..3090564..17518470..99301225..552967815
.14.196..966.4761.32775.225625.1369900..8317456..52895444.336392281.2102483853
.16.256.1392.7569.57681.439569.2956980.19891600.140048460.986022801.6826106385

Examples

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

Links

Crossrefs

Column 2 is A016742.
Column 3 is A086113.
Column 4 is A207399.
Row 1 is A006498(n+2).
Row 2 is A189145(n+2).

A207741 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 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, 15, 81, 114, 81, 14, 25, 225, 361, 387, 196, 22, 40, 625, 1425, 1849, 1414, 484, 35, 64, 1600, 5625, 10535, 10201, 5302, 1225, 56, 104, 4096, 20550, 60025, 86355, 58081, 20265, 3136, 90, 169, 10816, 75076, 327075, 731025
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2....4.....6.......9.......15.........25..........40............64
..4...16....36......81......225........625........1600..........4096
..6...36...114.....361.....1425.......5625.......20550.........75076
..9...81...387....1849....10535......60025......327075.......1782225
.14..196..1414...10201....86355.....731025.....5959350......48580900
.22..484..5302...58081...733363....9259849...113534330....1392036100
.35.1225.20265..335241..6349893..120275089..2215586241...40813292529
.56.3136.78120.1946025.55343835.1573946929.43590708750.1207251562500

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Column 3 is A207712
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)
Row 3 is A207427

A207858 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 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, 15, 81, 102, 100, 16, 25, 225, 289, 370, 256, 26, 40, 625, 1071, 1369, 1232, 676, 42, 64, 1600, 3969, 7289, 5929, 4238, 1764, 68, 104, 4096, 13230, 38809, 44121, 26569, 14406, 4624, 110, 169, 10816, 44100, 178088, 328329
Offset: 1

Views

Author

R. H. Hardin Feb 21 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
.10..100...370...1369.....7289.....38809.....178088......817216.......3976696
.16..256..1232...5929....44121....328329....2047902....12773476......85393582
.26..676..4238..26569...279219...2934369...24999522...212984836....1971051046
.42.1764.14406.117649..1737981..25674489..298294290..3465676900...44249929850
.68.4624.49164.522729.10873197.226171521.3584335104.56804048896.1001624438528

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207249
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)
Row 3 is A207704
Showing 1-10 of 18 results. Next

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

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