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 1-5 of 5 results.

A298055 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 73, 73, 34, 95, 13, 21, 177, 63, 141, 121, 141, 63, 177, 21, 34, 359, 96, 240, 231, 231, 240, 96, 359, 34, 55, 705, 147, 428, 422, 512, 422, 428, 147, 705, 55, 89, 1351, 233
Offset: 1

Views

Author

R. H. Hardin, Jan 11 2018

Keywords

Comments

Table starts
..0...1...1...2....3....5....8....13....21....34.....55.....89....144.....233
..1...3...7..13...23...49...95...177...359...705...1351...2689...5303...10321
..1...7..15..19...23...34...63....96...147...233....368....588....933....1500
..2..13..19..40...73..141..240...428...779..1531...2989...5729..10760...20205
..3..23..23..73..121..231..422...865..1729..3286...6319..12563..24164...46151
..5..49..34.141..231..512..780..1577..3162..6228..12289..24231..47917...95955
..8..95..63.240..422..780.1708..3362..6794.14943..29523..61474.128150..264417
.13.177..96.428..865.1577.3362..7014.15247.34464..71665.153171.337793..727538
.21.359.147.779.1729.3162.6794.15247.35804.81453.182350.407843.937627.2114521

Examples

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

Links

Crossrefs

Column 1 is A000045(n-1).
Column 2 is A297852.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
k=3: [order 18] for n>19
k=4: [order 72] for n>73

A298093 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 7 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 21, 30, 21, 49, 8, 13, 95, 33, 53, 53, 33, 95, 13, 21, 177, 53, 92, 45, 92, 53, 177, 21, 34, 359, 77, 149, 87, 87, 149, 77, 359, 34, 55, 705, 111, 250, 150, 171, 150, 250, 111, 705, 55, 89, 1351, 171, 426
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2018

Keywords

Comments

Table starts
..0...1...1...2...3...5...8..13..21...34...55...89..144...233...377...610...987
..1...3...7..13..23..49..95.177.359..705.1351.2689.5303.10321.20423.40353.79223
..1...7..15..19..21..33..53..77.111..171..269..415..643..1013..1605..2543..4041
..2..13..19..30..53..92.149.250.426..809.1456.2602.4606..8096.14731.27112.49118
..3..23..21..53..45..87.150.216.249..423..711..980.1560..2431..3368..5598..8655
..5..49..33..92..87.171.203.328.484..782.1106.1905.2833..4428..7210.11516.17938
..8..95..53.149.150.203.229.365.410..734..917.1484.2077..2943..4659..7326.10594
.13.177..77.250.216.328.365.417.593..783.1086.1490.1929..2529..3490..4795..6787
.21.359.111.426.249.484.410.593.822.1041.1437.2208.3116..4525..6831.10816.16439

Examples

			Some solutions for n=7 k=4
..0..1..0..0. .0..1..0..0. .0..0..0..1. .0..1..0..1. .0..0..1..0
..0..1..1..1. .1..0..1..1. .0..1..0..1. .0..1..0..1. .1..1..0..1
..1..0..1..0. .0..1..0..1. .1..1..0..0. .0..1..0..1. .1..0..1..0
..1..0..1..0. .1..0..1..1. .1..1..0..0. .1..1..1..0. .1..1..1..0
..0..1..1..1. .0..1..0..0. .0..1..0..1. .0..0..1..0. .1..1..1..0
..0..1..0..0. .1..0..1..0. .1..0..1..0. .1..1..0..1. .1..0..1..0
..0..1..1..0. .1..0..0..0. .0..1..0..1. .1..0..1..0. .0..0..1..1

Links

Crossrefs

Column 1 is A000045(n-1).
Column 2 is A297852.
Column 3 is A297853.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
k=3: a(n) = 2*a(n-1) -a(n-4) -a(n-5) -a(n-6) +a(n-7) +a(n-8) for n>9
k=4: [order 35] for n>40
k=5: [order 82] for n>86

A298660 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 85, 85, 34, 95, 13, 21, 177, 63, 173, 177, 173, 63, 177, 21, 34, 359, 96, 322, 431, 431, 322, 96, 359, 34, 55, 705, 147, 635, 876, 1116, 876, 635, 147, 705, 55, 89, 1351
Offset: 1

Views

Author

R. H. Hardin, Jan 24 2018

Keywords

Comments

Table starts
..0...1...1....2....3.....5.....8.....13......21......34.......55........89
..1...3...7...13...23....49....95....177.....359.....705.....1351......2689
..1...7..15...19...23....34....63.....96.....147.....233......368.......588
..2..13..19...40...85...173...322....635....1325....2806.....5877.....12293
..3..23..23...85..177...431...876...2137....5002...11687....27591.....64253
..5..49..34..173..431..1116..2562...6711...17405...48462...125671....334571
..8..95..63..322..876..2562..7964..24801...74358..242072...745571...2349275
.13.177..96..635.2137..6711.24801..89543..322065.1213296..4468276..16453935
.21.359.147.1325.5002.17405.74358.322065.1367704.6098314.26543249.116098205

Examples

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

Links

Crossrefs

Column 1 is A000045(n-1).
Column 2 is A297852.
Column 3 is A298050.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
k=3: [order 18] for n>19
k=4: [order 72] for n>73

A299612 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 85, 85, 34, 95, 13, 21, 177, 63, 173, 179, 173, 63, 177, 21, 34, 359, 96, 322, 453, 453, 322, 96, 359, 34, 55, 705, 147, 635, 1006, 1223, 1006, 635, 147, 705, 55, 89, 1351
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2018

Keywords

Comments

Table starts
..0...1...1....2....3.....5......8......13......21.......34........55
..1...3...7...13...23....49.....95.....177.....359......705......1351
..1...7..15...19...23....34.....63......96.....147......233.......368
..2..13..19...40...85...173....322.....635....1325.....2806......5877
..3..23..23...85..179...453...1006....2523....6002....14802.....36299
..5..49..34..173..453..1223...3286....9873...28227....86428....253623
..8..95..63..322.1006..3286..13490...49047..183585...713699...2714170
.13.177..96..635.2523..9873..49047..231838.1084038..5339757..25938953
.21.359.147.1325.6002.28227.183585.1084038.6506278.41165944.255972254

Examples

			Some solutions for n=6 k=6
..0..1..1..1..0..1. .0..1..1..0..0..0. .0..1..0..1..0..0. .0..1..0..1..1..0
..0..0..1..1..1..0. .0..0..0..0..0..1. .0..1..0..1..0..1. .0..1..0..0..0..0
..1..1..1..1..1..1. .0..0..0..0..1..0. .1..1..1..1..1..1. .0..1..0..0..0..0
..0..0..1..1..1..1. .1..0..0..0..0..1. .0..0..1..1..1..1. .1..0..0..0..0..1
..1..1..1..0..0..1. .0..1..0..1..0..1. .1..1..1..1..1..0. .1..0..1..0..0..1
..0..0..1..0..1..1. .0..1..0..1..0..0. .0..0..1..1..0..1. .0..1..0..1..0..1

Links

Crossrefs

Column 1 is A000045(n-1).
Column 2 is A297852.
Column 3 is A298050.
Column 4 is A298656.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
k=3: [order 18] for n>19
k=4: [order 72] for n>73

A298888 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 73, 73, 34, 95, 13, 21, 177, 63, 141, 123, 141, 63, 177, 21, 34, 359, 96, 240, 243, 243, 240, 96, 359, 34, 55, 705, 147, 428, 444, 516, 444, 428, 147, 705, 55, 89, 1351, 233
Offset: 1

Views

Author

R. H. Hardin, Jan 28 2018

Keywords

Comments

Table starts
..0...1...1...2....3....5....8....13....21....34.....55.....89.....144.....233
..1...3...7..13...23...49...95...177...359...705...1351...2689....5303...10321
..1...7..15..19...23...34...63....96...147...233....368....588.....933....1500
..2..13..19..40...73..141..240...428...779..1531...2989...5729...10760...20205
..3..23..23..73..123..243..444...897..1801..3462...6669..13291...25762...49483
..5..49..34.141..243..516..814..1646..3312..6565..13040..25941...51679..103895
..8..95..63.240..444..814.1818..3663..7496.16544..33596..70466..148451..311053
.13.177..96.428..897.1646.3663..7768.17225.39617..83996.184024..411042..903972
.21.359.147.779.1801.3312.7496.17225.41048.95996.221358.505218.1183870.2737277

Examples

			Some solutions for n=7 k=5
..0..1..0..0..0. .0..1..0..1..1. .0..0..1..0..1. .0..1..1..0..1
..0..0..1..1..1. .1..0..0..1..0. .1..0..1..1..0. .1..0..0..0..1
..0..0..0..0..0. .0..1..1..1..0. .1..0..0..0..1. .1..0..0..0..1
..1..0..0..0..1. .0..1..1..1..0. .1..0..0..0..1. .0..0..0..0..0
..1..0..0..0..1. .1..1..1..1..1. .0..0..0..0..0. .1..1..1..0..0
..0..1..1..0..1. .1..1..0..0..0. .1..1..1..0..0. .0..0..0..0..1
..1..0..1..0..0. .1..0..1..1..1. .0..0..0..1..0. .1..1..1..0..1

Links

Crossrefs

Column 1 is A000045(n-1).
Column 2 is A297852.
Column 3 is A298050.
Column 4 is A298051.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
k=3: [order 18] for n>19
k=4: [order 72] for n>73
Showing 1-5 of 5 results.

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