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.

A300472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 160, 108, 16, 32, 401, 925, 925, 401, 32, 64, 1490, 5363, 8608, 5363, 1490, 64, 128, 5536, 31106, 80914, 80914, 31106, 5536, 128, 256, 20569, 180397, 759100, 1231578, 759100, 180397, 20569, 256, 512, 76424, 1046223
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2018

Keywords

Comments

Table starts
...1.....2.......4.........8..........16............32..............64
...2.....8......29.......108.........401..........1490............5536
...4....29.....160.......925........5363.........31106..........180397
...8...108.....925......8608.......80914........759100.........7121067
..16...401....5363.....80914.....1231578......18735889.......284885784
..32..1490...31106....759100....18735889.....462538206.....11408562672
..64..5536..180397...7121067...284885784...11408562672....456303004550
.128.20569.1046223..66808673..4332278363..281433652906..18253046515989
.256.76424.6067629.626787854.65881928079.6942908646999.730219136878799

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A220547.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)
k=3: a(n) = 6*a(n-1) -a(n-2) -a(n-3) +a(n-4) -4*a(n-5) +a(n-6) -a(n-7)
k=4: [order 22]
k=5: [order 58] for n>59

A300811 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 170, 108, 16, 32, 401, 1004, 1004, 401, 32, 64, 1490, 5908, 9504, 5908, 1490, 64, 128, 5536, 34836, 90980, 90980, 34836, 5536, 128, 256, 20569, 205369, 872495, 1415898, 872495, 205369, 20569, 256, 512, 76424, 1210811
Offset: 1

Views

Author

R. H. Hardin, Mar 13 2018

Keywords

Comments

Table starts
...1.....2.......4.........8..........16............32..............64
...2.....8......29.......108.........401..........1490............5536
...4....29.....170......1004........5908.........34836..........205369
...8...108....1004......9504.......90980........872495.........8363710
..16...401....5908.....90980.....1415898......22066384.......343667594
..32..1490...34836....872495....22066384.....559634028.....14189038853
..64..5536..205369...8363710...343667594...14189038853....585611214958
.128.20569.1210811..80174942..5352803078..359766695966..24166702223161
.256.76424.7138574.768542846.83370618870.9121562946307.997271941003944

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A220547.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)
k=3: [order 13]
k=4: [order 40]

A301450 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 171, 108, 16, 32, 401, 1008, 1008, 401, 32, 64, 1490, 5930, 9541, 5930, 1490, 64, 128, 5536, 34976, 91370, 91370, 34976, 5536, 128, 256, 20569, 206266, 877044, 1423344, 877044, 206266, 20569, 256, 512, 76424, 1216562
Offset: 1

Views

Author

R. H. Hardin, Mar 21 2018

Keywords

Comments

Table starts
...1.....2.......4.........8..........16............32...............64
...2.....8......29.......108.........401..........1490.............5536
...4....29.....171......1008........5930.........34976...........206266
...8...108....1008......9541.......91370........877044..........8414314
..16...401....5930.....91370.....1423344......22207589........346263718
..32..1490...34976....877044....22207589.....564002959......14319674594
..64..5536..206266...8414314...346263718...14319674594.....592006690060
.128.20569.1216562..80726964..5399605493..363595763125...24472344492129
.256.76424.7175157.774477323.84198470831.9231743942243.1011614229196954

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A220547.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)
k=3: [order 13]
k=4: [order 40]

A326105 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 161, 108, 16, 32, 401, 929, 929, 401, 32, 64, 1490, 5383, 8628, 5383, 1490, 64, 128, 5536, 31236, 81088, 81088, 31236, 5536, 128, 256, 20569, 181227, 760989, 1233763, 760989, 181227, 20569, 256, 512, 76424, 1051456
Offset: 1

Views

Author

R. H. Hardin, Jun 06 2019

Keywords

Comments

Table starts
...1.....2.......4.........8..........16............32..............64
...2.....8......29.......108.........401..........1490............5536
...4....29.....161.......929........5383.........31236..........181227
...8...108.....929......8628.......81088........760989.........7140349
..16...401....5383.....81088.....1233763......18773244.......285501774
..32..1490...31236....760989....18773244.....463572941.....11436374461
..64..5536..181227...7140349...285501774...11436374461....457515856087
.128.20569.1051456..67004116..4342306378..282167817331..18304957522469
.256.76424.6100399.628759699.66044562508.6962226034753.732434052866467

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A220547.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)
k=3: a(n) = 5*a(n-1) +5*a(n-2) -2*a(n-3) -3*a(n-6) -2*a(n-7) -a(n-8) -a(n-9)
k=4: [order 22]
k=5: [order 59] for n>60
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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