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 1-4 of 4 results.

A302381 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 76, 34, 0, 5, 161, 430, 475, 111, 0, 8, 601, 2886, 4640, 2771, 361, 0, 13, 2208, 19215, 56541, 48980, 16451, 1172, 0, 21, 8053, 127535, 688999, 1089035, 514655, 97160, 3809, 0, 34, 29415, 847604, 8334338, 24209608, 20993054
Offset: 1

Views

Author

R. H. Hardin, Apr 06 2018

Keywords

Comments

Table starts
.0.....1.......1.........2............3..............5................8
.0.....3......15........46..........161............601.............2208
.0....11......76.......430.........2886..........19215...........127535
.0....34.....475......4640........56541.........688999..........8334338
.0...111....2771.....48980......1089035.......24209608........535192095
.0...361...16451....514655.....20993054......849467774......34271733937
.0..1172...97160...5421003....404225195....29810775827....2195619257236
.0..3809..574671..57068484...7787623959..1046322460741..140685735128595
.0.12377.3397622.600825641.150008013842.36721875744312.9013655138528774

Examples

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

Links

Crossrefs

Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A232077(n-1).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 11]
k=4: [order 26]
k=5: [order 84] for n>86
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
n=3: [order 14] for n>15
n=4: [order 42] for n>43

A302953 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 86, 34, 0, 5, 161, 519, 587, 111, 0, 8, 601, 3626, 6531, 3815, 361, 0, 13, 2208, 26167, 87901, 80589, 25131, 1172, 0, 21, 8053, 185810, 1248691, 2104533, 998670, 164916, 3809, 0, 34, 29415, 1317541, 17374552, 58679318
Offset: 1

Views

Author

R. H. Hardin, Apr 16 2018

Keywords

Comments

Table starts
.0.....1.......1..........2............3...............5..................8
.0.....3......15.........46..........161.............601...............2208
.0....11......86........519.........3626...........26167.............185810
.0....34.....587.......6531........87901.........1248691...........17374552
.0...111....3815......80589......2104533........58679318.........1596912288
.0...361...25131.....998670.....50519822......2766909379.......147310312318
.0..1172..164916...12365841...1212025201....130376252119.....13578993819785
.0..3809.1083375..153141597..29081585941...6144174797769...1251888966185979
.0.12377.7114906.1896492042.697771332458.289545909430332.115412264434282781

Examples

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

Links

Crossrefs

Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A232077(n-1).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: a(n) = 4*a(n-1) +15*a(n-2) +13*a(n-3) -2*a(n-4) -19*a(n-5) -3*a(n-6) +4*a(n-8)
k=4: [order 13]
k=5: [order 43] for n>44
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
n=3: [order 7] for n>9
n=4: [order 24] for n>25
n=5: [order 73] for n>74

A303102 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 77, 34, 0, 5, 161, 431, 486, 111, 0, 8, 601, 2913, 4667, 2869, 361, 0, 13, 2208, 19393, 58160, 49534, 17229, 1172, 0, 21, 8053, 128921, 709333, 1138331, 523578, 102952, 3809, 0, 34, 29415, 857789, 8650205, 25372284, 22292709
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2018

Keywords

Comments

Table starts
.0.....1.......1.........2............3..............5.................8
.0.....3......15........46..........161............601..............2208
.0....11......77.......431.........2913..........19393............128921
.0....34.....486......4667........58160.........709333...........8650205
.0...111....2869.....49534......1138331.......25372284.........568099880
.0...361...17229....523578.....22292709......906385523.......37220475492
.0..1172..102952...5550469....436394066....32409609245.....2441756629583
.0..3809..616065..58797885...8545589681..1158734336743...160164698180399
.0.12377.3685099.622939052.167325743073.41428642572259.10505922762123798

Examples

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

Links

Crossrefs

Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A232077(n-1).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 11]
k=4: [order 26]
k=5: [order 90] for n>91
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
n=3: [order 14] for n>15
n=4: [order 42] for n>43

A278208 T(n,k)=Number of nXk 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) (1,0) or (1,1), with upper left element zero.

Original entry on oeis.org

0, 0, 0, 0, 3, 0, 0, 15, 15, 0, 0, 46, 97, 46, 0, 0, 161, 666, 666, 161, 0, 0, 601, 4827, 8242, 4827, 601, 0, 0, 2208, 34869, 117088, 117088, 34869, 2208, 0, 0, 8053, 251260, 1674402, 3295771, 1674402, 251260, 8053, 0, 0, 29415, 1811189, 23732454, 93838003
Offset: 1

Views

Author

R. H. Hardin, Nov 15 2016

Keywords

Comments

Table starts
.0.....0........0..........0.............0...............0..................0
.0.....3.......15.........46...........161.............601...............2208
.0....15.......97........666..........4827...........34869.............251260
.0....46......666.......8242........117088.........1674402...........23732454
.0...161.....4827.....117088.......3295771........93838003.........2644587148
.0...601....34869....1674402......93838003......5306819216.......297169006604
.0..2208...251260...23732454....2644587148....297169006604.....33056811286568
.0..8053..1811189..336380248...74502577363..16636687338399...3676498268449668
.0.29415.13056663.4770344900.2100207846025.931945034345185.409137247202506544

Examples

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

Links

Crossrefs

Column 2 is A232077(n-1).

Formula

Empirical for column k:
k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
k=3: [order 8] for n>9
k=4: [order 19]
k=5: [order 48] for n>49
Showing 1-4 of 4 results.

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