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 1-8 of 8 results.

A302212 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 16, 3, 16, 1, 34, 5, 47, 6, 32, 1, 65, 32, 7, 147, 10, 64, 1, 123, 22, 111, 18, 386, 21, 128, 1, 266, 72, 80, 448, 55, 1065, 42, 256, 1, 499, 101, 424, 281, 1725, 172, 3063, 86, 512, 1, 1037, 216, 1157, 1868, 1395, 6423, 575, 8624, 179
Offset: 1

Views

Author

R. H. Hardin, Apr 03 2018

Keywords

Comments

Table starts
...1..1....1....1.....1......1.......1........1........1..........1...........1
...2..2...11...13....34.....65.....123......266......499.......1037........2042
...4..2...16....5....32.....22......72......101......216........486.........968
...8..3...47....7...111.....80.....424.....1157.....2922......12816.......33744
..16..6..147...18...448....281....1868.....6036....16344.....110672......332791
..32.10..386...55..1725...1395...11170....46215...142804....1296927.....3754619
..64.21.1065..172..6423...8756...55922...465040..1136003...19265064....60547641
.128.42.3063..575.24927..43128..291320..3509969..9080114..212347228...786789878
.256.86.8624.1962.96909.234170.1544411.29343177.73189971.2698247985.11028726211

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513(n-2).
Row 2 is A297870(n+2).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 9]
k=4: [order 28] for n>32
k=5: [order 37] for n>41
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 19] for n>20
n=4: [order 61] for n>62

A302460 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 18, 3, 16, 1, 34, 8, 55, 6, 32, 1, 65, 44, 10, 177, 10, 64, 1, 123, 56, 233, 54, 474, 21, 128, 1, 266, 140, 123, 924, 111, 1397, 42, 256, 1, 499, 364, 1518, 1096, 3875, 276, 4135, 86, 512, 1, 1037, 764, 2945, 8869, 5266, 17189, 1050
Offset: 1

Views

Author

R. H. Hardin, Apr 08 2018

Keywords

Comments

Table starts
...1..1.....1....1......1......1........1.........1..........1...........1
...2..2....11...13.....34.....65......123.......266........499........1037
...4..2....18....8.....44.....56......140.......364........764........2352
...8..3....55...10....233....123.....1518......2945......16711.......58462
..16..6...177...54....924...1096.....8869.....29770.....176077......900973
..32.10...474..111...3875...5266....61254....287294....2165323....15547748
..64.21..1397..276..17189..25285...404761...2588958...25019102...250630168
.128.42..4135.1050..72529.149381..2822737..26036557..322917567..4472928245
.256.86.11882.3589.300519.866961.19107381.258817075.4110999261.79010238897

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513(n-2).
Row 2 is A297870(n+2).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 12]
k=4: [order 71] for n>72
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 19] for n>20
n=4: [order 71] for n>72

A303242 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 18, 3, 16, 1, 34, 8, 55, 6, 32, 1, 65, 60, 10, 181, 10, 64, 1, 123, 56, 255, 61, 494, 21, 128, 1, 266, 236, 149, 1106, 160, 1465, 42, 256, 1, 499, 428, 1676, 1373, 5158, 458, 4415, 86, 512, 1, 1037, 1248, 3307, 11111, 7823, 23995, 1748
Offset: 1

Views

Author

R. H. Hardin, Apr 20 2018

Keywords

Comments

Table starts
...1..1.....1....1......1.......1........1.........1..........1............1
...2..2....11...13.....34......65......123.......266........499.........1037
...4..2....18....8.....60......56......236.......428.......1248.........3264
...8..3....55...10....255.....149.....1676......3307......18505........65498
..16..6...181...61...1106....1373....11111.....38480.....221943......1162591
..32.10...494..160...5158....7823....90728....421983....3251872.....23282610
..64.21..1465..458..23995...41878...686376...4288552...44547581....435326091
.128.42..4415.1748.108726..277018..5320294..48315454..648070597...8762716079
.256.86.12934.6056.506416.1721671.42575026.536745912.9508520220.176408218876

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513(n-2).
Row 2 is A297870(n+2).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13]
k=4: [order 71] for n>72
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 20]
n=4: [order 67] for n>68

A298259 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 1, 2, 0, 0, 11, 4, 4, 11, 0, 0, 13, 3, 11, 3, 13, 0, 0, 34, 7, 23, 23, 7, 34, 0, 0, 65, 14, 72, 86, 72, 14, 65, 0, 0, 123, 35, 201, 238, 238, 201, 35, 123, 0, 0, 266, 89, 597, 604, 895, 604, 597, 89, 266, 0, 0, 499, 242, 1705, 2492, 3335, 3335, 2492
Offset: 1

Views

Author

R. H. Hardin, Jan 15 2018

Keywords

Comments

Table starts
.0...0..0....0....0.....0......0.......0........0.........0.........0
.0...1..3....2...11....13.....34......65......123.......266.......499
.0...3..1....4....3.....7.....14......35.......89.......242.......643
.0...2..4...11...23....72....201.....597.....1705......5141.....15305
.0..11..3...23...86...238....604....2492.....7722.....26880.....93816
.0..13..7...72..238...895...3335...13980....55889....230402....953813
.0..34.14..201..604..3335..13991...70095...331341...1644480...8037526
.0..65.35..597.2492.13980..70095..435534..2412035..14299708..83146969
.0.123.89.1705.7722.55889.331341.2412035.16014301.112395697.777907073

Examples

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

Links

Crossrefs

Column 2 is A297870.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
k=3: [order 18] for n>19
k=4: [order 53] for n>54

A298087 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 0, 2, 0, 0, 11, 3, 3, 11, 0, 0, 13, 1, 10, 1, 13, 0, 0, 34, 7, 28, 28, 7, 34, 0, 0, 65, 18, 76, 154, 76, 18, 65, 0, 0, 123, 52, 213, 520, 520, 213, 52, 123, 0, 0, 266, 144, 645, 1574, 2767, 1574, 645, 144, 266, 0, 0, 499, 405, 1852, 7204, 11202
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2018

Keywords

Comments

Table starts
.0...0...0....0.....0......0.......0........0.........0..........0...........0
.0...1...3....2....11.....13......34.......65.......123........266.........499
.0...3...0....3.....1......7......18.......52.......144........405........1124
.0...2...3...10....28.....76.....213......645......1852.......5642.......17016
.0..11...1...28...154....520....1574.....7204.....28790.....105055......437163
.0..13...7...76...520...2767...11202....66148....385999....2040394....11280309
.0..34..18..213..1574..11202...65218...479206...3481050...24695892...177272585
.0..65..52..645..7204..66148..479206..4883926..46039875..420410890..3947485108
.0.123.144.1852.28790.385999.3481050.46039875.603770100.7267200831.90210295443

Examples

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

Links

Crossrefs

Column 2 is A297870.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
k=3: [order 16] for n>17
k=4: [order 57] for n>58

A298895 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 1, 2, 0, 0, 11, 4, 4, 11, 0, 0, 13, 4, 11, 4, 13, 0, 0, 34, 11, 31, 31, 11, 34, 0, 0, 65, 26, 80, 219, 80, 26, 65, 0, 0, 123, 66, 229, 579, 579, 229, 66, 123, 0, 0, 266, 171, 681, 1858, 2963, 1858, 681, 171, 266, 0, 0, 499, 462, 1969, 8891, 12224
Offset: 1

Views

Author

R. H. Hardin, Jan 28 2018

Keywords

Comments

Table starts
.0...0...0....0.....0......0.......0........0.........0..........0............0
.0...1...3....2....11.....13......34.......65.......123........266..........499
.0...3...1....4.....4.....11......26.......66.......171........462.........1248
.0...2...4...11....31.....80.....229......681......1969.......5973........18031
.0..11...4...31...219....579....1858.....8891.....34212.....128103.......538967
.0..13..11...80...579...2963...12224....72620....426475....2284203.....12768382
.0..34..26..229..1858..12224...74725...547497...4012035...28805843....209118279
.0..65..66..681..8891..72620..547497..5719782..54423404..502721390...4804572705
.0.123.171.1969.34212.426475.4012035.54423404.724538480.8857192378.112203393143

Examples

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

Links

Crossrefs

Column 2 is A297870.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
k=3: [order 17] for n>18
k=4: [order 58] for n>59

A298139 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 0, 2, 0, 0, 11, 3, 3, 11, 0, 0, 13, 0, 10, 0, 13, 0, 0, 34, 3, 20, 20, 3, 34, 0, 0, 65, 6, 68, 88, 68, 6, 65, 0, 0, 123, 23, 185, 242, 242, 185, 23, 123, 0, 0, 266, 68, 561, 627, 917, 627, 561, 68, 266, 0, 0, 499, 205, 1600, 2604, 3417, 3417, 2604
Offset: 1

Views

Author

R. H. Hardin, Jan 13 2018

Keywords

Comments

Table starts
.0...0..0....0....0.....0......0.......0........0.........0.........0
.0...1..3....2...11....13.....34......65......123.......266.......499
.0...3..0....3....0.....3......6......23.......68.......205.......572
.0...2..3...10...20....68....185.....561.....1600......4856.....14490
.0..11..0...20...88...242....627....2604.....8137.....28727....101137
.0..13..3...68..242...917...3417...14533....58845....244155...1024766
.0..34..6..185..627..3417..14422...73961...354200...1772595...8807624
.0..65.23..561.2604.14533..73961..467043..2633905..15796516..93682029
.0.123.68.1600.8137.58845.354200.2633905.17828062.127068717.899366629

Examples

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

Links

Crossrefs

Column 2 is A297870.
Column 3 is A297871.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
k=3: [order 17] for n>18
k=4: [order 60] for n>61

A298930 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 1, 2, 0, 0, 11, 4, 4, 11, 0, 0, 13, 3, 11, 3, 13, 0, 0, 34, 7, 23, 23, 7, 34, 0, 0, 65, 14, 72, 94, 72, 14, 65, 0, 0, 123, 35, 201, 255, 255, 201, 35, 123, 0, 0, 266, 89, 597, 666, 955, 666, 597, 89, 266, 0, 0, 499, 242, 1717, 2720, 3569, 3569, 2720
Offset: 1

Views

Author

R. H. Hardin, Jan 29 2018

Keywords

Comments

Table starts
.0...0..0....0....0.....0......0.......0........0.........0.........0
.0...1..3....2...11....13.....34......65......123.......266.......499
.0...3..1....4....3.....7.....14......35.......89.......242.......643
.0...2..4...11...23....72....201.....597.....1717......5183.....15479
.0..11..3...23...94...255....666....2720.....8571.....30093....106192
.0..13..7...72..255...955...3569...15031....61046....253624...1067751
.0..34.14..201..666..3569..15163...77576...375845...1886321...9434661
.0..65.35..597.2720.15031..77576..491338..2806944..16889645.100996053
.0.123.89.1717.8571.61046.375845.2806944.19329083.138482223.988954778

Examples

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

Links

Crossrefs

Column 2 is A297870.
Column 3 is A298254.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
k=3: [order 18] for n>19
k=4: [order 60] for n>61
Showing 1-8 of 8 results.

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