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 1-7 of 7 results.

A184756 Half the number of n X 4 binary arrays with no 1 having an adjacent 1 both above and to its left.

Original entry on oeis.org

8, 89, 1056, 12397, 145778, 1713803, 20148584, 236878817, 2784890782, 32740859687, 384921344068, 4525368067837, 53202963328218, 625486206737315, 7353594054643744, 86453298151112665, 1016397248157274582
Offset: 1

Views

Author

R. H. Hardin, Jan 21 2011

Keywords

Comments

Column 4 of A184761.

Examples

			Some solutions for 3 X 4:
..1..1..0..0....0..1..1..1....1..0..1..0....0..1..1..0....0..1..0..1
..1..0..0..1....0..0..0..0....0..1..0..0....1..0..0..1....0..1..0..0
..1..1..1..0....0..0..0..1....0..0..0..1....1..1..0..0....0..1..1..0

Links

Crossrefs

Cf. A184761.

Formula

Empirical: a(n) = 8*a(n-1) + 39*a(n-2) + 58*a(n-3) + 32*a(n-4).
Empirical g.f.: x*(8 + 25*x + 32*x^2 + 14*x^3) / (1 - 8*x - 39*x^2 - 58*x^3 - 32*x^4). - Colin Barker, Feb 27 2018

A184754 Half the number of n X n binary arrays with no 1 having an adjacent 1 both above and to its left.

Original entry on oeis.org

1, 7, 163, 12397, 3110914, 2568513843, 6982256142285, 62483420093901107, 1840782554883258104105, 178527915853668578288219231, 57000185549334885919706636039360, 59911857895558455825087768017439269698
Offset: 1

Views

Author

R. H. Hardin Jan 21 2011

Keywords

Comments

Diagonal of A184761

Examples

			Some solutions for 3X3
..1..1..0....1..1..1....1..1..0....1..0..1....1..0..1....0..0..1....0..1..1
..0..1..0....1..0..1....0..1..1....1..1..0....1..0..1....0..0..0....1..0..1
..0..1..0....1..1..0....1..0..0....0..0..0....1..0..0....1..1..0....0..0..0

Links

A184755 Half the number of n X 3 binary arrays with no 1 having an adjacent 1 both above and to its left.

Original entry on oeis.org

4, 25, 163, 1056, 6847, 44391, 287802, 1865917, 12097367, 78431296, 508496451, 3296753387, 21373960178, 138574567177, 898425491035, 5824794400480, 37764099690423, 244837350020575, 1587362824918602, 10291406673539877
Offset: 1

Views

Author

R. H. Hardin, Jan 21 2011

Keywords

Comments

Column 3 of A184761.

Examples

			Some solutions for 5 X 3:
..0..1..0....1..0..1....1..1..0....1..0..0....0..0..0....0..1..1....1..1..0
..0..1..0....1..0..1....1..0..0....0..1..0....1..1..1....1..0..0....1..0..1
..0..1..0....1..0..1....0..1..0....0..0..1....1..0..0....0..1..1....0..1..0
..0..1..0....1..0..1....0..1..0....0..0..0....1..0..0....1..0..0....0..0..0
..0..0..0....1..0..0....1..0..0....0..1..0....1..1..1....1..0..1....1..1..0

Links

Crossrefs

Cf. A184761.

Formula

Empirical: a(n) = 5*a(n-1) + 9*a(n-2) + 4*a(n-3).
Empirical g.f.: x*(4 + 5*x + 2*x^2) / (1 - 5*x - 9*x^2 - 4*x^3). - Colin Barker, Apr 14 2018

A184757 Half the number of n X 5 binary arrays with no 1 having an adjacent 1 both above and to its left.

Original entry on oeis.org

16, 317, 6847, 145778, 3110914, 66363023, 1415755252, 30202770902, 644326291402, 13745636657969, 293240447607511, 6255800447755343, 133457166530876185, 2847088145920628222, 60737921547191898319, 1295743203159170280830
Offset: 1

Views

Author

R. H. Hardin, Jan 21 2011

Keywords

Comments

Column 5 of A184761.

Examples

			Some solutions for 3 X 5:
..1..1..0..0..0....0..0..0..0..0....1..0..1..0..1....0..0..1..1..1
..0..0..1..0..0....0..0..0..1..1....1..0..1..1..0....1..1..0..0..1
..0..0..1..0..0....0..0..0..1..0....1..1..0..1..0....1..0..0..0..0

Links

Crossrefs

Cf. A184761.

Formula

Empirical: a(n) = 13*a(n-1) + 150*a(n-2) + 550*a(n-3) + 889*a(n-4) + 434*a(n-5) - 228*a(n-6) + 32*a(n-7).
Empirical g.f.: x*(16 + 109*x + 326*x^2 + 417*x^3 + 176*x^4 - 166*x^5 + 40*x^6) / (1 - 13*x - 150*x^2 - 550*x^3 - 889*x^4 - 434*x^5 + 228*x^6 - 32*x^7). - Colin Barker, Apr 14 2018

A184758 Half the number of nX6 binary arrays with no 1 having an adjacent 1 both above and to its left.

Original entry on oeis.org

32, 1129, 44391, 1713803, 66363023, 2568513843, 99419347147, 3848174315295, 148949599913987, 5765325542821919, 223155884726125003, 8637595276083930107, 334331547130486255947, 12940822049109738429467, 500894626143397858765227
Offset: 1

Views

Author

R. H. Hardin Jan 21 2011

Keywords

Comments

Column 6 of A184761

Examples

			Some solutions for 3X6
..0..0..1..0..0..0....0..1..1..1..0..0....0..0..0..1..0..1....0..0..1..1..1..0
..0..0..1..0..0..1....1..0..0..0..0..1....1..1..1..0..0..0....0..0..0..0..1..0
..0..0..1..0..1..0....0..1..0..1..0..1....0..0..1..1..1..1....0..0..1..0..1..1

Links

A184759 Half the number of nX7 binary arrays with no 1 having an adjacent 1 both above and to its left.

Original entry on oeis.org

64, 4021, 287802, 20148584, 1415755252, 99419347147, 6982256142285, 490358739919898, 34437619490245450, 2418533807739519677, 169852219543126318591, 11928622276532341733243, 837740183488415335215180
Offset: 1

Views

Author

R. H. Hardin Jan 21 2011

Keywords

Comments

Column 7 of A184761

Examples

			Some solutions for 3X7
..0..1..0..1..0..1..0....0..0..1..0..0..1..1....0..1..0..1..1..0..0
..0..0..1..0..1..0..0....0..0..0..1..1..0..0....0..1..0..0..1..0..0
..0..1..0..0..1..0..1....1..0..0..0..1..1..0....0..0..0..0..0..1..1

Links

A184760 Half the number of nX8 binary arrays with no 1 having an adjacent 1 both above and to its left.

Original entry on oeis.org

128, 14321, 1865917, 236878817, 30202770902, 3848174315295, 490358739919898, 62483420093901107, 7961905153672004774, 1014539579452170241886, 129276927715415033559253, 16473013159661022852279611
Offset: 1

Views

Author

R. H. Hardin Jan 21 2011

Keywords

Comments

Column 8 of A184761

Examples

			Some solutions for 3X8
..0..0..1..0..0..0..0..1....0..0..0..0..1..0..0..1....0..0..0..1..1..0..1..1
..0..0..0..0..0..0..0..1....0..0..0..1..0..0..0..1....0..0..0..0..0..0..1..0
..0..0..1..1..1..1..0..0....0..0..0..0..0..0..1..0....0..0..1..1..0..0..1..1

Links

Showing 1-7 of 7 results.

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