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.

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A219156 T(n,k)=Unchanging value maps: number of nXk binary arrays indicating the locations of corresponding elements unequal to no horizontal, antidiagonal or vertical neighbor in a random 0..1 nXk array.

Original entry on oeis.org

1, 2, 2, 4, 4, 4, 7, 9, 9, 7, 12, 21, 32, 21, 12, 21, 49, 104, 104, 49, 21, 37, 115, 360, 531, 360, 115, 37, 65, 269, 1234, 2708, 2708, 1234, 269, 65, 114, 628, 4224, 13725, 20400, 13725, 4224, 628, 114, 200, 1468, 14421, 69784, 153666, 153666, 69784, 14421, 1468
Offset: 1

Views

Author

R. H. Hardin Nov 12 2012

Keywords

Comments

Table starts
...1.....2.......4.........7..........12............21..............37
...2.....4.......9........21..........49...........115.............269
...4.....9......32.......104.........360..........1234............4224
...7....21.....104.......531........2708.........13725...........69784
..12....49.....360......2708.......20400........153666.........1158374
..21...115....1234.....13725......153666.......1707676........19027977
..37...269....4224.....69784.....1158374......19027977.......313358793
..65...628...14421....354500.....8729263.....212185508......5166391614
.114..1468...49292...1800573....65770098....2364398926.....85169635842
.200..3433..168568...9147029...495575471...26340590202...1403453366899
.351..8025..576373..46470551..3734568186..293506138765..23126821932330
.616.18758.1970380.236075721.28142976424.3270741315594.381141272070008

Examples

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

Links

Crossrefs

Column 1 is A005251(n+2)

A220226 T(n,k)=Majority value maps: number of nXk binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 nXk array.

Original entry on oeis.org

1, 2, 1, 4, 6, 1, 7, 18, 19, 1, 12, 51, 115, 65, 1, 21, 157, 694, 697, 222, 1, 37, 477, 4244, 8819, 4406, 776, 1, 65, 1445, 25771, 103153, 110911, 27584, 2682, 1, 114, 4384, 156627, 1198517, 2517202, 1409467, 173216, 9310, 1, 200, 13297, 952152, 13984325
Offset: 1

Views

Author

R. H. Hardin Dec 08 2012

Keywords

Comments

Table starts
.1.....2.......4........7.......12.......21.........37........65.....114...200
.1.....6......18.......51......157......477.......1445......4384...13297.40332
.1....19.....115......694.....4244....25771.....156627....952152.5791155
.1....65.....697.....8819...103153..1198517...13984325.162860081
.1...222....4406...110911..2517202.56154702.1256395206
.1...776...27584..1409467.61669499
.1..2682..173216.17911553
.1..9310.1087102
.1.32288
.1

Examples

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

Links

Crossrefs

Column 2 is A220065
Row 1 is A005251(n+2)

A220406 T(n,k)=Equals two maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 nXk array.

Original entry on oeis.org

1, 1, 1, 2, 6, 1, 4, 17, 23, 1, 7, 40, 122, 78, 1, 12, 93, 908, 720, 292, 1, 21, 206, 6013, 10989, 4304, 1066, 1, 37, 431, 41510, 128448, 139233, 25391, 3922, 1, 65, 924, 273253, 1701214, 2996186, 1782679, 150079, 14420, 1, 114, 1863, 1851686, 20736643
Offset: 1

Views

Author

R. H. Hardin Dec 13 2012

Keywords

Comments

Table starts
.1.....1......2........4........7.......12.......21........37.......65..114.200
.1.....6.....17.......40.......93......206......431.......924.....1863.3898
.1....23....122......908.....6013....41510...273253...1851686.12276677
.1....78....720....10989...128448..1701214.20736643.263993960
.1...292...4304...139233..2996186.76047436
.1..1066..25391..1782679.74035199
.1..3922.150079.22578152
.1.14420.884793
.1.53082
.1

Examples

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

Links

Crossrefs

Column 2 is A220238
Row 1 is A005251(n+1)

A231382 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

Original entry on oeis.org

2, 2, 2, 4, 10, 4, 7, 21, 21, 7, 12, 48, 93, 48, 12, 21, 113, 378, 378, 113, 21, 37, 261, 1519, 2539, 1519, 261, 37, 65, 601, 6126, 17363, 17363, 6126, 601, 65, 114, 1390, 24747, 120124, 209118, 120124, 24747, 1390, 114, 200, 3216, 99964, 830890, 2547810
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Table starts
...2....2.......4.........7..........12.............21...............37
...2...10......21........48.........113............261..............601
...4...21......93.......378........1519...........6126............24747
...7...48.....378......2539.......17363.........120124...........830890
..12..113....1519.....17363......209118........2547810.........30936914
..21..261....6126....120124.....2547810.......54485279.......1157805351
..37..601...24747....830890....30936914.....1157805351......42978519280
..65.1390...99964...5746499...375620622....24615811883....1597438228604
.114.3216..403743..39745115..4560995236...523548909308...59402875813957
.200.7435.1630662.274872588.55375119088.11133382117666.2208383979206654

Examples

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

Links

Crossrefs

Column 1 is A005251(n+2)

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5) for n>6
k=3: [order 10] for n>11
k=4: [order 19] for n>20
k=5: [order 46] for n>47

A231515 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

Original entry on oeis.org

2, 2, 2, 4, 6, 4, 7, 14, 14, 7, 12, 35, 78, 35, 12, 21, 90, 343, 343, 90, 21, 37, 225, 1537, 2594, 1537, 225, 37, 65, 569, 7505, 19435, 19435, 7505, 569, 65, 114, 1441, 35872, 158061, 256846, 158061, 35872, 1441, 114, 200, 3640, 168887, 1275558, 3691558
Offset: 1

Views

Author

R. H. Hardin, Nov 09 2013

Keywords

Comments

Table starts
...2....2.......4.........7...........12.............21...............37
...2....6......14........35...........90............225..............569
...4...14......78.......343.........1537...........7505............35872
...7...35.....343......2594........19435.........158061..........1275558
..12...90....1537.....19435.......256846........3691558.........51741521
..21..225....7505....158061......3691558.......97188562.......2438335793
..37..569...35872...1275558.....51741521.....2438335793.....108221463798
..65.1441..168887..10130742....714951561....59978232085....4680280632866
.114.3640..800573..80645991...9949033842..1495872774439..205954365382497
.200.9208.3806573.644138583.138737920339.37400468849958.9095707696345723

Examples

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

Links

Crossrefs

Column 1 is A005251(n+2)

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
k=2: a(n) = 2*a(n-1) +a(n-2) +3*a(n-3) -4*a(n-4) -2*a(n-5) -4*a(n-6)
k=3: [order 16] for n>17
k=4: [order 34] for n>35

A231544 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors.

Original entry on oeis.org

2, 2, 2, 4, 6, 4, 7, 20, 20, 7, 12, 57, 116, 57, 12, 21, 164, 589, 589, 164, 21, 37, 485, 3001, 5235, 3001, 485, 37, 65, 1424, 15644, 46122, 46122, 15644, 1424, 65, 114, 4169, 81179, 417298, 698721, 417298, 81179, 4169, 114, 200, 12228, 420243, 3763223, 10928292
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Table starts
...2.....2........4..........7...........12..............21................37
...2.....6.......20.........57..........164.............485..............1424
...4....20......116........589.........3001...........15644.............81179
...7....57......589.......5235........46122..........417298...........3763223
..12...164.....3001......46122.......698721........10928292.........170393737
..21...485....15644.....417298.....10928292.......296647240........8028429092
..37..1424....81179....3763223....170393737......8028429092......377320795091
..65..4169...420243...33812753...2643967833....216093538039....17623244476340
.114.12228..2177937..304137386..41079980720...5824887373442...824325064919737
.200.35868.11287977.2736503160.638622184605.157116139854017.38588079925163243

Examples

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

Links

Crossrefs

Column 1 is A005251(n+2)

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
k=2: a(n) = 4*a(n-1) -4*a(n-2) +5*a(n-3) -8*a(n-4) +3*a(n-5) -2*a(n-6) +a(n-7) -a(n-8)
k=3: [order 22]
k=4: [order 61]

A237859 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors.

Original entry on oeis.org

2, 4, 4, 7, 14, 7, 12, 41, 41, 12, 21, 114, 184, 114, 21, 37, 325, 773, 773, 325, 37, 65, 943, 3373, 4826, 3373, 943, 65, 114, 2731, 15038, 31651, 31651, 15038, 2731, 114, 200, 7876, 66838, 213165, 315896, 213165, 66838, 7876, 200, 351, 22702, 295601, 1428967
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2014

Keywords

Comments

Table starts
...2.....4.......7........12..........21............37..............65
...4....14......41.......114.........325...........943............2731
...7....41.....184.......773........3373.........15038...........66838
..12...114.....773......4826.......31651........213165.........1428967
..21...325....3373.....31651......315896.......3255233........33328972
..37...943...15038....213165.....3255233......51576880.......810629762
..65..2731...66838...1428967....33328972.....810629762.....19525964230
.114..7876..295601...9520138...338653847...12628484789....465620654717
.200.22702.1306735..63406826..3440498469..196722783963..11103987320260
.351.65489.5781785.422805151.35005538562.3069861742669.265336172863532

Examples

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

Links

Crossrefs

Column 1 is A005251(n+3)

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) +2*a(n-4) +a(n-5)
k=3: [order 11]
k=4: [order 21]
k=5: [order 46]
k=6: [order 98]

A242584 T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern aabb (with a!=b) and new values 0..k introduced in 0..k order.

Original entry on oeis.org

7, 13, 12, 14, 35, 21, 14, 45, 97, 37, 14, 46, 159, 271, 65, 14, 46, 174, 587, 757, 114, 14, 46, 175, 723, 2209, 2115, 200, 14, 46, 175, 744, 3192, 8391, 5913, 351, 14, 46, 175, 745, 3453, 14648, 32020, 16535, 616, 14, 46, 175, 745, 3481, 17178, 68819, 122439, 46237
Offset: 1

Views

Author

R. H. Hardin, May 17 2014

Keywords

Comments

Table starts
....7.....13......14......14.......14.......14.......14.......14.......14
...12.....35......45......46.......46.......46.......46.......46.......46
...21.....97.....159.....174......175......175......175......175......175
...37....271.....587.....723......744......745......745......745......745
...65....757....2209....3192.....3453.....3481.....3482.....3482.....3482
..114...2115....8391...14648....17178....17634....17670....17671....17671
..200...5913...32020...68819....90033....95729....96472....96517....96518
..351..16535..122439..327821...489821...550503...562109...563256...563311
..616..46237..468605.1574161..2734513..3316400..3469255..3491141..3492837
.1081.129291.1794215.7594177.15534111.20716789.22511261.22860029.22898822

Examples

			Some solutions for n=4 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....0....1....1....1....1
..0....2....0....2....2....2....2....2....2....2....2....1....1....2....2....2
..2....1....2....2....3....0....0....3....3....1....3....2....1....1....0....2
..1....2....0....0....4....3....3....0....3....0....4....3....2....3....2....3
..3....3....0....3....1....3....2....4....3....3....3....2....1....3....3....4
..2....2....3....4....2....4....4....3....2....1....3....1....2....0....4....0

Links

Crossrefs

Column 1 is A005251(n+5)

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
k=2: a(n) = 4*a(n-1) -5*a(n-2) +6*a(n-3) -4*a(n-4)
k=3: a(n) = 7*a(n-1) -18*a(n-2) +32*a(n-3) -45*a(n-4) +37*a(n-5) -21*a(n-6) +9*a(n-7)
k=4: [order 10]
k=5: [order 13]
k=6: [order 16]
k=7: [order 19]

A243389 T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern abba (with a!=b) and new values 0..k introduced in 0..k order.

Original entry on oeis.org

7, 13, 12, 14, 35, 21, 14, 45, 96, 37, 14, 46, 158, 265, 65, 14, 46, 173, 579, 733, 114, 14, 46, 174, 715, 2165, 2029, 200, 14, 46, 174, 736, 3145, 8173, 5618, 351, 14, 46, 174, 737, 3406, 14384, 30991, 15557, 616, 14, 46, 174, 737, 3434, 16910, 67346, 117755, 43081
Offset: 1

Views

Author

R. H. Hardin, Jun 04 2014

Keywords

Comments

Table starts
....7.....13......14......14.......14.......14.......14.......14.......14
...12.....35......45......46.......46.......46.......46.......46.......46
...21.....96.....158.....173......174......174......174......174......174
...37....265.....579.....715......736......737......737......737......737
...65....733....2165....3145.....3406.....3434.....3435.....3435.....3435
..114...2029....8173...14384....16910....17366....17402....17403....17403
..200...5618...30991...67346....88473....94164....94907....94952....94953
..351..15557..117755..319672...480524...541060...552660...553807...553862
..616..43081..447850.1529489..2677917..3257286..3409915..3431794..3433490
.1081.119303.1704019.7351421.15183903.20333069.22122613.22471051.22509836

Examples

			Some solutions for n=3 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....1....1....1....0....1....0....1....1....1....1....1....1....1
..2....1....1....2....1....2....1....2....1....0....2....2....1....2....2....0
..3....0....2....3....2....2....1....0....2....1....3....3....1....2....0....2
..2....1....0....4....0....2....1....3....0....2....0....3....2....2....3....1
..4....1....1....0....3....0....2....3....3....2....2....1....0....1....4....1

Links

Crossrefs

Column 1 is A005251(n+5)

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
k=2: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-3) -a(n-4)
k=3: a(n) = 7*a(n-1) -16*a(n-2) +18*a(n-3) -15*a(n-4) +9*a(n-5) -3*a(n-6) +a(n-7)
k=4: [order 10]
k=5: [order 13]
k=6: [order 16]
k=7: [order 19]

A295531 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

Original entry on oeis.org

1, 2, 2, 4, 10, 4, 7, 29, 29, 7, 12, 87, 147, 87, 12, 21, 280, 774, 774, 280, 21, 37, 876, 4080, 7071, 4080, 876, 37, 65, 2735, 21489, 64189, 64189, 21489, 2735, 65, 114, 8583, 113466, 588529, 1012315, 588529, 113466, 8583, 114, 200, 26900, 598374, 5400933
Offset: 1

Views

Author

R. H. Hardin, Nov 23 2017

Keywords

Comments

Table starts
...1.....2.......4.........7..........12............21...............37
...2....10......29........87.........280...........876.............2735
...4....29.....147.......774........4080.........21489...........113466
...7....87.....774......7071.......64189........588529..........5400933
..12...280....4080.....64189.....1012315......16031147........253594307
..21...876...21489....588529....16031147.....437241277......11938414614
..37..2735..113466...5400933...253594307...11938414614.....563330031268
..65..8583..598374..49414072..4003959566..325438086413...26515589323171
.114.26900.3155426.452274232.63279327977.8875686431050.1248681784524804

Examples

			Some solutions for n=5 k=4
..0..1..1..1. .1..1..0..1. .0..0..1..1. .1..1..1..0. .0..1..1..0
..0..1..0..1. .1..0..0..1. .0..0..0..1. .0..0..0..1. .0..0..0..0
..1..1..0..0. .0..1..1..0. .1..0..0..1. .1..1..0..1. .1..1..0..0
..0..0..1..1. .1..1..1..0. .1..0..0..0. .1..0..0..1. .0..1..0..1
..0..0..1..1. .1..1..0..0. .0..1..1..0. .1..1..1..0. .0..1..1..1

Links

Crossrefs

Column 1 is A005251(n+2).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
k=3: [order 18]
k=4: [order 45]
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