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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A219002 T(n,k)=Unmatched value maps: number of nXk binary arrays indicating the locations of corresponding elements not equal to any horizontal, diagonal or antidiagonal neighbor in a random 0..2 nXk array.

Original entry on oeis.org

1, 2, 1, 4, 10, 1, 7, 46, 36, 1, 12, 163, 328, 126, 1, 21, 604, 2265, 2374, 454, 1, 37, 2341, 16648, 31857, 17776, 1632, 1, 65, 9019, 127401, 462668, 461681, 131548, 5854, 1, 114, 34489, 966981, 7027671, 13259232, 6639893, 973492, 21010, 1, 200, 131968, 7298225
Offset: 1

Views

Author

R. H. Hardin Nov 09 2012

Keywords

Comments

Table starts
.1......2........4..........7..........12..........21..........37...........65
.1.....10.......46........163.........604........2341........9019........34489
.1.....36......328.......2265.......16648......127401......966981......7298225
.1....126.....2374......31857......462668.....7027671...105807897...1583929029
.1....454....17776.....461681....13259232...401608939.12030873701.357976038469
.1...1632...131548....6639893...377629096.22776074699
.1...5854...973492...95431043.10745153084
.1..21010..7213582.1372612359
.1..75412.53429692
.1.270662
.1

Examples

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

Links

Crossrefs

Column 2 is A202796
Row 1 is A005251(n+2)

A219410 T(n,k)=Unmatched value maps: number of nXk binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..2 nXk array.

Original entry on oeis.org

1, 2, 1, 4, 7, 1, 7, 28, 21, 1, 12, 98, 181, 65, 1, 21, 351, 1199, 1180, 200, 1, 37, 1261, 8173, 14737, 7687, 616, 1, 65, 4523, 57097, 193116, 181089, 50077, 1897, 1, 114, 16233, 398375, 2633596, 4560446, 2225293, 326233, 5842, 1, 200, 58268, 2773933
Offset: 1

Views

Author

R. H. Hardin Nov 19 2012

Keywords

Comments

Table starts
.1......2..........4............7.............12..............21
.1......7.........28...........98............351............1261
.1.....21........181.........1199...........8173...........57097
.1.....65.......1180........14737.........193116.........2633596
.1....200.......7687.......181089........4560446.......121641579
.1....616......50077......2225293......107701719......5618116265
.1...1897.....326233.....27345143.....2543481662....259468310384
.1...5842....2125270....336026564....60067211485..11983486642214
.1..17991...13845268...4129209727..1418553120783.553453107750115
.1..55405...90196219..50741147949.33500701298909
.1.170625..587591326.623524656508
.1.525456.3827916001

Examples

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

Links

Crossrefs

Column 2 is A218836
Row 1 is A005251(n+2)

A220386 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 and antidiagonal neighbors in a random 0..1 nXk array.

Original entry on oeis.org

1, 2, 1, 4, 7, 1, 7, 25, 21, 1, 12, 79, 136, 65, 1, 21, 278, 757, 753, 200, 1, 37, 966, 5114, 7462, 4160, 616, 1, 65, 3362, 33247, 96772, 73066, 22989, 1897, 1, 114, 11642, 211944, 1191846, 1829169, 715412, 127037, 5842, 1, 200, 40375, 1358599, 14300020
Offset: 1

Views

Author

R. H. Hardin Dec 13 2012

Keywords

Comments

Table starts
.1......2.........4...........7............12.............21..............37
.1......7........25..........79...........278............966............3362
.1.....21.......136.........757..........5114..........33247..........211944
.1.....65.......753........7462.........96772........1191846........14300020
.1....200......4160.......73066.......1829169.......42415575.......953142266
.1....616.....22989......715412......34521416.....1509240923.....63512364783
.1...1897....127037.....7003040.....651568437....53692543412...4230913273170
.1...5842....702009....68557435...12297040231..1910141303899.281832304026762
.1..17991...3879313...671141189..232084431547.67952729355483
.1..55405..21437148..6570141318.4380156648582
.1.170625.118462034.64318370539
.1.525456.654623158

Examples

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

Links

Crossrefs

Column 2 is A218836
Row 1 is A005251(n+2)

A221035 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 and antidiagonal neighbors in a random 0..2 nXk array.

Original entry on oeis.org

1, 2, 1, 4, 7, 1, 7, 33, 21, 1, 12, 119, 228, 65, 1, 21, 457, 1733, 1561, 200, 1, 37, 1710, 14277, 24485, 10648, 616, 1, 65, 6466, 110506, 419506, 345755, 72625, 1897, 1, 114, 24433, 870027, 6637755, 12239631, 4882030, 495329, 5842, 1, 200, 92196, 6717882
Offset: 1

Views

Author

R. H. Hardin Dec 29 2012

Keywords

Comments

Table starts
.1......2.........4...........7...........12............21............37
.1......7........33.........119..........457..........1710..........6466
.1.....21.......228........1733........14277........110506........870027
.1.....65......1561.......24485.......419506.......6637755.....106761517
.1....200.....10648......345755.....12239631.....393788081...12843452050
.1....616.....72625.....4882030....356411031...23287585899.1537391091350
.1...1897....495329....68933905..10373626389.1376083439034
.1...5842...3378333...973340015.301896920812
.1..17991..23041525.13743460075
.1..55405.157152036
.1.170625
.1

Examples

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

Links

Crossrefs

Column 2 is A218836
Row 1 is A005251(n+2)

A231523 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

2, 2, 4, 4, 10, 8, 7, 34, 21, 16, 12, 107, 153, 48, 32, 21, 342, 865, 776, 113, 64, 37, 1069, 4665, 7697, 3861, 261, 128, 65, 3381, 25556, 70462, 66499, 18721, 601, 256, 114, 10689, 144847, 680302, 1031105, 571226, 91993, 1390, 512, 200, 33808, 817539
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Table starts
....2....2........4..........7...........12..............21................37
....4...10.......34........107..........342............1069..............3381
....8...21......153........865.........4665...........25556............144847
...16...48......776.......7697........70462..........680302...........6935963
...32..113.....3861......66499......1031105........17572772.........322599407
...64..261....18721.....571226.....15000701.......451200772.......14940780666
..128..601....91993....4944075....219937967.....11683058939......697702378939
..256.1390...453274...42759650...3222629836....302190345444....32529760276112
..512.3216..2223662..369356733..47159743290...7806399525348..1514885617016157
.1024.7435.10915727.3191749214.690399979855.201765495180944.70592106166184098

Examples

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

Links

Crossrefs

Column 1 is A000079
Column 2 is A231376
Row 1 is A005251(n+2)

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
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 13] for n>14
k=4: [order 24] for n>25
k=5: [order 70] for n>71
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
n=2: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) +6*a(n-4) -18*a(n-5)
n=3: [order 16] for n>17
n=4: [order 39] for n>40

A232047 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

2, 2, 4, 4, 7, 8, 7, 15, 21, 16, 12, 34, 80, 65, 32, 21, 79, 318, 446, 200, 64, 37, 184, 1315, 3082, 2477, 616, 128, 65, 426, 5364, 22063, 29974, 13752, 1897, 256, 114, 984, 21680, 153562, 377676, 290672, 76375, 5842, 512, 200, 2274, 87452, 1060850, 4588174
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2013

Keywords

Comments

Table starts
....2.....2........4..........7...........12..............21................37
....4.....7.......15.........34...........79.............184...............426
....8....21.......80........318.........1315............5364.............21680
...16....65......446.......3082........22063..........153562...........1060850
...32...200.....2477......29974.......377676.........4588174..........55505057
...64...616....13752.....290672......6430408.......136134243........2882322121
..128..1897....76375....2821630....109609484......4041385884......149582129861
..256..5842...424115...27382537...1868028342....119990644449.....7766282047395
..512.17991..2355221..265752221..31836538191...3562337669985...403179428472169
.1024.55405.13079032.2579134666.542586883485.105762437152368.20931014633412316

Examples

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

Links

Crossrefs

Column 1 is A000079
Column 2 is A218836
Row 1 is A005251(n+2)

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3)
k=3: a(n) = 4*a(n-1) +9*a(n-2) -a(n-3) -6*a(n-4) for n>5
k=4: [order 8] for n>9
k=5: [order 14] for n>15
k=6: [order 24] for n>26
k=7: [order 44] for n>47
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
n=2: a(n) = 4*a(n-1) -6*a(n-2) +7*a(n-3) -6*a(n-4) +3*a(n-5) -a(n-6) -a(n-7) for n>8
n=3: [order 15] for n>18
n=4: [order 33] for n>36
n=5: [order 78] for n>84

A297314 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

1, 2, 1, 4, 7, 1, 7, 23, 21, 1, 12, 66, 117, 65, 1, 21, 207, 497, 609, 200, 1, 37, 654, 2577, 3808, 3159, 616, 1, 65, 2049, 13937, 35476, 29212, 16389, 1897, 1, 114, 6422, 72541, 340825, 484808, 223995, 85041, 5842, 1, 200, 20119, 375054, 2997197, 8273245
Offset: 1

Views

Author

R. H. Hardin, Dec 28 2017

Keywords

Comments

Table starts
.1.....2.......4.........7..........12............21..............37
.1.....7......23........66.........207...........654............2049
.1....21.....117.......497........2577.........13937...........72541
.1....65.....609......3808.......35476........340825.........2997197
.1...200....3159.....29212......484808.......8273245.......121339476
.1...616...16389....223995.....6623719.....200646607......4893232934
.1..1897...85041...1717882....90535227....4869858862....197589351469
.1..5842..441225..13174266..1237278512..118156684121...7976248015498
.1.17991.2289339.101033369.16909630099.2867120332406.322003901582689

Examples

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

Links

Crossrefs

Column 2 is A218836.
Row 1 is A005251(n+2).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3)
k=3: a(n) = 3*a(n-1) +11*a(n-2) +3*a(n-3) -6*a(n-4)
k=4: [order 8] for n>9
k=5: [order 12] for n>14
k=6: [order 22] for n>25
k=7: [order 35] for n>39
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
n=2: [order 9]
n=3: [order 23]
n=4: [order 61]

A297506 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

1, 2, 1, 4, 10, 1, 7, 31, 29, 1, 12, 68, 110, 87, 1, 21, 218, 314, 531, 280, 1, 37, 729, 1829, 2281, 2534, 876, 1, 65, 2097, 8803, 23348, 14201, 11405, 2735, 1, 114, 6139, 34757, 191192, 270845, 88808, 53175, 8583, 1, 200, 18932, 157673, 1247716, 3624914
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2017

Keywords

Comments

Table starts
.1.....2.......4........7.........12...........21.............37
.1....10......31.......68........218..........729...........2097
.1....29.....110......314.......1829.........8803..........34757
.1....87.....531.....2281......23348.......191192........1247716
.1...280....2534....14201.....270845......3624914.......35049871
.1...876...11405....88808....3075264.....66289769......978288822
.1..2735...53175...573119...35919085...1272836591....28914051279
.1..8583..246040..3613793..414559944..23896899569...823340493402
.1.26900.1135117.22999331.4794512057.450529429259.23748019543354

Examples

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

Links

Crossrefs

Column 2 is A295525.
Row 1 is A005251(n+2).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
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 11]
k=4: [order 18]
k=5: [order 50]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
n=2: a(n) = 3*a(n-1) -2*a(n-2) +9*a(n-3) -6*a(n-4) -8*a(n-5)
n=3: [order 10]
n=4: [order 24]
n=5: [order 59]

A297654 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 3 neighboring 1s.

Original entry on oeis.org

1, 2, 1, 4, 10, 1, 7, 43, 36, 1, 12, 140, 231, 126, 1, 21, 494, 1073, 1421, 454, 1, 37, 1845, 6838, 11024, 9033, 1632, 1, 65, 6757, 45036, 131044, 113252, 55706, 5854, 1, 114, 24479, 268655, 1580681, 2525244, 1105531, 346032, 21010, 1, 200, 89068, 1617465
Offset: 1

Views

Author

R. H. Hardin, Jan 02 2018

Keywords

Comments

Table starts
.1.....2........4..........7...........12.............21................37
.1....10.......43........140..........494...........1845..............6757
.1....36......231.......1073.........6838..........45036............268655
.1...126.....1421......11024.......131044........1580681..........16899640
.1...454.....9033.....113252......2525244.......56630842........1075678445
.1..1632....55706....1105531.....46187510.....1906300826.......63350980838
.1..5854...346032...11089103....864944851....65775301075.....3863740405975
.1.21010..2151932..110654243..16149058068..2265577299182...234680441414485
.1.75412.13364992.1101808354.300870617401.77814433907002.14203234114710492

Examples

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

Links

Crossrefs

Column 2 is A202796.
Row 1 is A005251(n+2).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3)
k=3: [order 11]
k=4: [order 24]
k=5: [order 60]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
n=2: a(n) = 3*a(n-1) -2*a(n-2) +13*a(n-3) +6*a(n-4) +12*a(n-5) +12*a(n-6)
n=3: [order 17]
n=4: [order 38]

A297720 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 4 neighboring 1s.

Original entry on oeis.org

1, 2, 1, 4, 10, 1, 7, 34, 29, 1, 12, 83, 145, 87, 1, 21, 258, 523, 747, 280, 1, 37, 865, 2717, 4212, 4090, 876, 1, 65, 2651, 14462, 36981, 34319, 21116, 2735, 1, 114, 8041, 68919, 336653, 512354, 268630, 110551, 8583, 1, 200, 25114, 332306, 2699832, 8103241
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2018

Keywords

Comments

Table starts
.1.....2.......4.........7..........12............21..............37
.1....10......34........83.........258...........865............2651
.1....29.....145.......523........2717.........14462...........68919
.1....87.....747......4212.......36981........336653.........2699832
.1...280....4090.....34319......512354.......8103241.......107787351
.1...876...21116....268630.....6812856.....183324631......4021047904
.1..2735..110551...2139403....91994155....4238895126....154327332017
.1..8583..582755..17031173..1242370107...98184350818...5920531350715
.1.26900.3055652.135252357.16741579726.2265008802005.226188909640209

Examples

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

Links

Crossrefs

Column 2 is A295525.
Row 1 is A005251(n+2).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
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 13]
k=4: [order 42]
k=5: [order 87]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
n=2: a(n) = 4*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4) -24*a(n-5) +24*a(n-6)
n=3: [order 18]
n=4: [order 51]
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