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.

A207928 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 10, 15, 81, 72, 100, 16, 25, 225, 144, 240, 256, 26, 40, 625, 360, 576, 704, 676, 42, 64, 1600, 900, 1872, 1936, 2080, 1764, 68, 104, 4096, 2160, 6084, 7744, 6400, 6216, 4624, 110, 169, 10816, 5184, 18096, 30976, 29760, 21904
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4.....6.....9.....15......25.......40........64.......104........169
..4...16....36....81....225.....625.....1600......4096.....10816......28561
..6...36....72...144....360.....900.....2160......5184.....12528......30276
.10..100...240...576...1872....6084....18096.....53824....165648.....509796
.16..256...704..1936...7744...30976...111584....401956...1513992....5702544
.26..676..2080..6400..29760..138384...592968...2540836..11151624...48944016
.42.1764..6216.21904.126688..732736..3773248..19430464.105642128..574369156
.68.4624.18496.73984.520608.3663396.22906752.143233024.955190016.6369955344

Examples

			Some solutions for n=9 k=3
..0..0..1....0..0..1....0..1..1....1..0..0....1..0..0....0..0..1....0..0..1
..0..1..1....1..1..1....0..0..1....1..0..0....0..0..1....1..1..1....0..0..1
..1..1..0....1..0..0....1..0..0....0..1..1....1..1..0....1..1..0....1..1..0
..1..0..0....0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..1..1
..0..1..1....1..1..0....1..1..1....1..1..0....0..0..1....1..0..1....1..0..0
..0..1..1....0..0..1....1..0..0....1..0..0....1..1..0....1..1..0....0..1..1
..1..0..0....1..0..0....0..1..1....0..1..1....0..1..1....0..1..1....1..0..1
..1..1..0....1..1..1....1..1..1....1..0..0....0..0..1....0..0..1....1..0..0
..0..1..1....0..1..1....1..0..0....1..1..1....1..0..0....1..1..0....0..1..1

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207840
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)

A208069 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 72, 81, 12, 26, 256, 240, 144, 144, 16, 42, 676, 704, 576, 216, 256, 20, 68, 1764, 2080, 1936, 1008, 324, 400, 25, 110, 4624, 6216, 6400, 3696, 1764, 432, 625, 30, 178, 12100, 18496, 21904, 12960, 7056, 2688, 576, 900, 36
Offset: 1

Views

Author

R. H. Hardin Feb 23 2012

Keywords

Comments

Table starts
..2...4...6...10....16....26.....42......68.....110......178.......288
..4..16..36..100...256...676...1764....4624...12100....31684.....82944
..6..36..72..240...704..2080...6216...18496...55000...163760....487296
..9..81.144..576..1936..6400..21904...73984..250000...846400...2862864
.12.144.216.1008..3696.12960..48840..179520..657000..2423280...8913456
.16.256.324.1764..7056.26244.108900..435600.1726596..6937956..27751824
.20.400.432.2688.11424.44064.198000..844800.3542544.15213984..64859616
.25.625.576.4096.18496.73984.360000.1638400.7268416.33362176.151585344

Examples

			Some solutions for n=4 k=3
..0..0..1....0..1..0....1..1..0....1..1..0....0..1..0....1..1..0....1..0..0
..0..1..1....1..0..1....1..0..1....1..1..0....0..0..1....1..1..0....0..0..1
..0..0..1....0..1..0....1..0..0....1..1..0....0..1..0....1..0..0....1..0..0
..0..1..0....1..0..0....0..0..1....1..1..0....0..0..1....1..1..0....0..0..1

Links

Crossrefs

Column 1 is A002620(n+2)
Column 2 is A030179(n+2)
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A207840
Row 4 is A207924

A208379 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 8, 16, 100, 72, 64, 10, 26, 256, 240, 108, 100, 12, 42, 676, 704, 420, 144, 144, 14, 68, 1764, 2080, 1344, 640, 180, 196, 16, 110, 4624, 6216, 4212, 2176, 900, 216, 256, 18, 178, 12100, 18496, 13860, 7072, 3200, 1200, 252, 324, 20, 288
Offset: 1

Views

Author

R. H. Hardin Feb 25 2012

Keywords

Comments

Table starts
..2...4...6...10...16....26....42.....68.....110.....178......288......466
..4..16..36..100..256...676..1764...4624...12100...31684....82944...217156
..6..36..72..240..704..2080..6216..18496...55000..163760...487296..1450192
..8..64.108..420.1344..4212.13860..44880..144540..468852..1517184..4906980
.10.100.144..640.2176..7072.25200..87040..296560.1028128..3545856.12198016
.12.144.180..900.3200.10660.40740.148240..526900.1931300..7015680.25336420
.14.196.216.1200.4416.14976.60984.231744..851400.3276624.12438144.46737936
.16.256.252.1540.5824.20020.86436.340816.1285900.5170900.20393856.79220932

Examples

			Some solutions for n=4 k=3
..0..1..0....0..1..1....1..1..0....0..0..1....0..0..1....1..0..1....1..0..0
..1..1..0....0..1..1....1..1..0....0..1..1....1..0..1....1..1..0....1..0..0
..1..1..0....0..0..1....1..1..0....0..1..0....0..0..1....0..1..0....1..0..0
..1..0..0....0..0..1....1..1..0....0..1..0....0..0..1....0..1..0....1..0..0

Links

Crossrefs

Column 1 is A004275(n+1)
Column 2 is A016742
Column 3 is A044102(n-1) for n>1
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A207840

Formula

Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = 36*n - 36 for n>1
k=4: a(n) = 20*n^2 + 40*n - 60 for n>1
k=5: a(n) = 96*n^2 - 32*n - 64 for n>1
k=6: a(n) = 364*n^2 - 416*n + 52 for n>1
k=7: a(n) = 84*n^3 + 840*n^2 - 1344*n + 420 for n>1
Empirical for row n:
n=1: a(k)=a(k-1)+a(k-2)
n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3)
n=3: a(k)=a(k-1)+4*a(k-2)+5*a(k-3)+2*a(k-4)-a(k-5)+a(k-6) for k>8
n=4: a(k)=a(k-1)+4*a(k-2)+9*a(k-3)+5*a(k-4)-2*a(k-5)+4*a(k-6) for k>8
n=5: a(k)=a(k-1)+4*a(k-2)+13*a(k-3)+8*a(k-4)-3*a(k-5)+9*a(k-6) for k>8
n=6: a(k)=a(k-1)+4*a(k-2)+17*a(k-3)+11*a(k-4)-4*a(k-5)+16*a(k-6) for k>8
n=7: a(k)=a(k-1)+4*a(k-2)+21*a(k-3)+14*a(k-4)-5*a(k-5)+25*a(k-6) for k>8
Showing 1-3 of 3 results.

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