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

A207111 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 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, 13, 81, 98, 64, 10, 18, 169, 271, 200, 100, 12, 25, 324, 677, 643, 350, 144, 14, 34, 625, 1504, 1835, 1271, 556, 196, 16, 46, 1156, 3399, 4534, 4047, 2239, 826, 256, 18, 62, 2116, 7220, 11511, 10898, 7837, 3641, 1168, 324, 20, 83, 3844
Offset: 1

Views

Author

R. H. Hardin Feb 15 2012

Keywords

Comments

Table starts
..2...4....6....9....13....18.....25.....34......46......62.......83......111
..4..16...36...81...169...324....625...1156....2116....3844.....6889....12321
..6..36...98..271...677..1504...3399...7220...15184...31664....64749...132543
..8..64..200..643..1835..4534..11511..27012...62814..144676...325111...733469
.10.100..350.1271..4047.10898..30415..77326..194952..486102..1177409..2870021
.12.144..556.2239..7837.22714..68737.187054..505040.1346150..3472283..9030485
.14.196..826.3641.13863.42874.139341.402498.1153962.3259098..8878431.24420005
.16.256.1168.5581.22931.75198.260597.794118.2402578.7142988.20426983.59031673

Examples

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

Links

Crossrefs

Column 2 is A016742
Row 1 is A171861(n+1)
Row 2 is A207025

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) = (7/60)*n^5 + (8/3)*n^4 + (185/12)*n^3 + (19/3)*n^2 - (218/15)*n + 3
k=6: a(n) = (7/360)*n^6 + (77/120)*n^5 + (635/72)*n^4 + (623/24)*n^3 - (511/180)*n^2 - (103/5)*n + 6
k=7: a(n) = (1/280)*n^7 + (7/45)*n^6 + (47/15)*n^5 + (206/9)*n^4 + (4111/120)*n^3 - (1037/45)*n^2 - (4493/210)*n + 9

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

A207346 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 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, 13, 81, 84, 100, 16, 18, 169, 192, 292, 256, 26, 25, 324, 426, 828, 912, 676, 42, 34, 625, 858, 2190, 3130, 2812, 1764, 68, 46, 1156, 1704, 5290, 9668, 11230, 8928, 4624, 110, 62, 2116, 3330, 12292, 27022, 41112, 43260, 28152
Offset: 1

Views

Author

R. H. Hardin Feb 17 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....84....192....426.....858.....1704.....3330......6390.....12150
.10..100...292....828...2190....5290....12292....27978.....62574....136978
.16..256...912...3130...9668...27022....71344...185624....468864...1161400
.26..676..2812..11230..41112..128292...388134..1134282...3225374...9002616
.42.1764..8928..43260.186002..684324..2367656..8000806..26057006..82907430
.68.4624.28152.163710.828530.3524736.13950908.53882188.199473062.720751822

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Row 1 is A171861(n+1)
Row 2 is A207025

A207589 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 60, 81, 13, 26, 256, 144, 144, 169, 18, 42, 676, 324, 432, 312, 324, 25, 68, 1764, 756, 1098, 1014, 612, 625, 34, 110, 4624, 1728, 3150, 3094, 2232, 1250, 1156, 46, 178, 12100, 3996, 8244, 9698, 7272, 5000, 2516, 2116, 62
Offset: 1

Views

Author

R. H. Hardin, Feb 19 2012

Keywords

Comments

Table starts
..2....4....6....10....16.....26.....42......68......110......178.......288
..4...16...36...100...256....676...1764....4624....12100....31684.....82944
..6...36...60...144...324....756...1728....3996.....9180....21168.....48708
..9...81..144...432..1098...3150...8244...23202....61560...171468....458640
.13..169..312..1014..3094...9698..30056...93782...291304...908102...2822456
.18..324..612..2232..7272..25776..85536..300096..1004364..3501756..11782620
.25..625.1250..5000.18150..70800.263550.1018700..3824100.14714500..55475900
.34.1156.2516.11220.46716.204476.876860.3832616.16578128.72435844.314466680

Examples

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

Links

Crossrefs

Column 1 is A171861(n+1).
Column 2 is A207025.
Row 1 is A006355(n+2).
Row 2 is A206981.

A207368 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 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 90, 81, 12, 18, 169, 252, 225, 144, 16, 25, 324, 624, 784, 420, 256, 20, 34, 625, 1350, 2304, 1736, 784, 400, 25, 46, 1156, 3025, 5625, 5856, 3844, 1260, 625, 30, 62, 2116, 6256, 14641, 15525, 14884, 7130, 2025, 900, 36, 83
Offset: 1

Views

Author

R. H. Hardin Feb 17 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...90...252...624...1350...3025....6256...12788....25792....50630
..9..81..225...784..2304...5625..14641...33856...77284...173056...372100
.12.144..420..1736..5856..15525..45738..115368..287174...700960..1620770
.16.256..784..3844.14884..42849.142884..393129.1067089..2839225..7059649
.20.400.1260..7130.31110..95220.353808.1047717.3056647..8773795.23208895
.25.625.2025.13225.65025.211600.876096.2792241.8755681.27112849.76300225

Examples

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

Links

Crossrefs

Column 1 is A002620(n+2)
Column 2 is A030179(n+2)
Row 1 is A171861(n+1)
Row 2 is A207025
Row 3 is A207026

A207467 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 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, 18, 169, 271, 358, 256, 26, 25, 324, 677, 1307, 1152, 676, 42, 34, 625, 1504, 4219, 5369, 3910, 1764, 68, 46, 1156, 3399, 11760, 21517, 23645, 12994, 4624, 110, 62, 2116, 7220, 33393, 71928, 119965, 101233
Offset: 1

Views

Author

R. H. Hardin Feb 18 2012

Keywords

Comments

Table starts
..2....4.....6......9......13.......18........25........34.........46
..4...16....36.....81.....169......324.......625......1156.......2116
..6...36....98....271.....677.....1504......3399......7220......15184
.10..100...358...1307....4219....11760.....33393.....88198.....229458
.16..256..1152...5369...21517....71928....247631....778010....2406006
.26..676..3910..23645..119965...491948...2090927...7990970...29983194
.42.1764.12994.101233..644401..3205650..16675001..76629370..345252578
.68.4624.43596.439063.3523073.21396734.136803627.760840082.4139073950

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Row 1 is A171861(n+1)
Row 2 is A207025
Row 3 is A207112

A207488 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 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, 13, 81, 82, 81, 14, 18, 169, 217, 177, 196, 22, 25, 324, 499, 530, 408, 484, 35, 34, 625, 1014, 1322, 1459, 942, 1225, 56, 46, 1156, 2141, 2749, 4041, 3947, 2233, 3136, 90, 62, 2116, 4188, 6217, 8808, 12151, 11306, 5348, 8100, 145, 83
Offset: 1

Views

Author

R. H. Hardin Feb 18 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..177...530...1322...2749...6217...12712...25908....52474...103704
.14..196..408..1459...4041...8808..21991...48044..105558...230156...490287
.22..484..942..3947..12151..26980..73325..170276..397692...935992..2150515
.35.1225.2233.11306..39050..89417.268275..667760.1691526..4324858.10910668
.56.3136.5348.32445.126411.292136.959855.2555724.6929562.19404152.53733153

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A171861(n+1)
Row 2 is A207025
Row 3 is A207270

A207500 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 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, 13, 81, 102, 81, 14, 18, 169, 283, 297, 196, 22, 25, 324, 699, 1004, 932, 484, 35, 34, 625, 1526, 2942, 3939, 2974, 1225, 56, 46, 1156, 3355, 7305, 14253, 15495, 9723, 3136, 90, 62, 2116, 6888, 17911, 41938, 68745, 62530, 32164
Offset: 1

Views

Author

R. H. Hardin Feb 18 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...297...1004....2942....7305....17911.....40262.....87990.....187012
.14..196...932...3939...14253...41938...122061....319798....813724....2009628
.22..484..2974..15495...68745..237576...804887...2408502...6896518...18962878
.35.1225..9723..62530..343310.1413961..5715255..20090516..67370124..216796950
.56.3136.32164.253747.1714707.8384076.40046975.163471950.628620128.2300337450

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A171861(n+1)
Row 2 is A207025
Row 3 is A207243

A207682 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 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, 13, 81, 72, 81, 13, 19, 169, 164, 166, 169, 18, 28, 361, 336, 436, 360, 324, 25, 41, 784, 702, 964, 1030, 660, 625, 34, 60, 1681, 1488, 2132, 2310, 2032, 1292, 1156, 46, 88, 3600, 3164, 4846, 5704, 4728, 4174, 2400, 2116, 62, 129
Offset: 1

Views

Author

R. H. Hardin Feb 19 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..166..436...964..2132...4846..11301..25496...57407..131250...299913
.13..169..360.1030..2310..5704..14090..34245..81936..201951..490844..1183972
.18..324..660.2032..4728.11994..29982..77141.193184..485658.1213580..3090430
.25..625.1292.4174..9450.25076..65564.171382.433468.1150747.2968284..7722348
.34.1156.2400.8266.18940.52632.139730.379618.990368.2737864.7139792.19521802

Examples

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

Links

Crossrefs

Column 1 is A171861(n+1)
Column 2 is A207025
Column 3 is A207509
Row 1 is A000930(n+3)
Row 2 is A207170
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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