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.

A302808 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 169, 128, 16, 32, 384, 934, 1010, 512, 32, 64, 1405, 5117, 8718, 6084, 2048, 64, 128, 5135, 28128, 74072, 82367, 36456, 8192, 128, 256, 18766, 154494, 632004, 1089773, 773520, 218640, 32768, 256, 512, 68589, 848519
Offset: 1

Views

Author

R. H. Hardin, Apr 13 2018

Keywords

Comments

Table starts
...1......2.......4.........8..........16............32..............64
...2......8......29.......105.........384..........1405............5135
...4.....32.....169.......934........5117.........28128..........154494
...8....128....1010......8718.......74072........632004.........5396562
..16....512....6084.....82367.....1089773......14458177.......192211013
..32...2048...36456....773520....15904814.....327603711......6769884156
..64...8192..218640...7267160...232260380....7428713676....238687785290
.128..32768.1312416..68346451..3396923500..168777255305...8434497360938
.256.131072.7873344.642498696.49653502029.3832039683236.297820640670676

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A302266.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 6*a(n-1) +24*a(n-3) -144*a(n-4) for n>6
k=4: [order 18] for n>20
k=5: [order 90] for n>92
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 13] for n>15
n=4: [order 48] for n>50

A302965 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 154, 128, 16, 32, 384, 786, 833, 512, 32, 64, 1405, 3924, 6206, 4527, 2048, 64, 128, 5135, 19868, 43588, 49521, 24602, 8192, 128, 256, 18766, 100161, 314989, 493132, 395493, 133757, 32768, 256, 512, 68589, 505908
Offset: 1

Views

Author

R. H. Hardin, Apr 16 2018

Keywords

Comments

Table starts
...1......2.......4.........8.........16...........32.............64
...2......8......29.......105........384.........1405...........5135
...4.....32.....154.......786.......3924........19868.........100161
...8....128.....833......6206......43588.......314989........2257439
..16....512....4527.....49521.....493132......5122000.......52646395
..32...2048...24602....395493....5602382.....83644490.....1233435694
..64...8192..133757...3157171...63612987...1365216668....28906043997
.128..32768..727293..25208524..722646394..22301032112...677939939546
.256.131072.3954552.201291251.8212135689.364489574945.15913688413086

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A302266.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) -7*a(n-2) -56*a(n-4) +64*a(n-5) for n>6
k=4: [order 19] for n>20
k=5: [order 80] for n>81
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 12] for n>13
n=4: [order 44] for n>45

A303469 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 170, 128, 16, 32, 384, 948, 1033, 512, 32, 64, 1405, 5237, 9110, 6369, 2048, 64, 128, 5135, 29009, 79377, 89371, 39098, 8192, 128, 256, 18766, 160590, 692636, 1243692, 872026, 240109, 32768, 256, 512, 68589, 888993
Offset: 1

Views

Author

R. H. Hardin, Apr 24 2018

Keywords

Comments

Table starts
...1......2.......4.........8..........16............32..............64
...2......8......29.......105.........384..........1405............5135
...4.....32.....170.......948........5237.........29009..........160590
...8....128....1033......9110.......79377........692636.........6051850
..16....512....6369.....89371.....1243692......17247543.......239939422
..32...2048...39098....872026....19374638.....427097893......9459086839
..64...8192..240109...8511918...302023677...10589284528....373571747330
.128..32768.1476141..83188773..4716032889..263136262937..14793218857797
.256.131072.9071642.812770434.73624207904.6538180319944.585806882371397

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A302266.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) -5*a(n-2) +20*a(n-3) -144*a(n-4) +72*a(n-5) for n>6
k=4: [order 20] for n>21
k=5: [order 93] for n>94
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 14] for n>15
n=4: [order 49] for n>50
Showing 1-3 of 3 results.

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