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 1-3 of 3 results.

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)

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]

A295416 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

Original entry on oeis.org

1, 2, 2, 4, 10, 4, 7, 36, 36, 7, 12, 126, 234, 126, 12, 21, 454, 1534, 1534, 454, 21, 37, 1632, 10291, 19026, 10291, 1632, 37, 65, 5854, 68613, 240439, 240439, 68613, 5854, 65, 114, 21010, 457178, 3019079, 5741797, 3019079, 457178, 21010, 114, 200, 75412
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2017

Keywords

Comments

Table starts
...1.....2........4..........7............12..............21.................37
...2....10.......36........126...........454............1632...............5854
...4....36......234.......1534.........10291...........68613.............457178
...7...126.....1534......19026........240439.........3019079...........37927609
..12...454....10291.....240439.......5741797.......136204120.........3232240913
..21..1632....68613....3019079.....136204120......6093564449.......272714953724
..37..5854...457178...37927609....3232240913....272714953724.....23025368248778
..65.21010..3048314..476686533...76727059034..12210363190599...1945003010538968
.114.75412.20323497.5990217198.1821136011730.546643613178667.164274708080518128

Examples

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

Links

Crossrefs

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

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) +a(n-2) +4*a(n-3)
k=3: a(n) = 6*a(n-1) +28*a(n-3) +3*a(n-4) +49*a(n-5) +33*a(n-6) -34*a(n-7) -22*a(n-8)
k=4: [order 14]
k=5: [order 37]
k=6: [order 78]
Showing 1-3 of 3 results.

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