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.

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A069439 Half the number of 13 X n binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

Original entry on oeis.org

4095, 33440190, 271523097884, 2192221953687972
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069440 Half the number of n X 2 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

Original entry on oeis.org

0, 2, 16, 88, 414, 1810, 7616, 31376, 127710, 516170, 2077552, 8341288, 33440190, 133941922, 536205056, 2145876128, 8586053694, 34350369050, 137416333936, 549701205496, 2198891419230, 8795774741170, 35183603690432, 140735633277488, 562945474867230
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Links

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

Formula

From Colin Barker, May 22 2012: (Start)
a(n) = 7*a(n-1) - 13*a(n-2) + 3*a(n-3) + 4*a(n-4).
G.f.: 2*x^2*(1+x+x^2)/((1-x)*(1-4*x)*(1-2*x-x^2)). (End)
a(n) = 2^(2*n-1) - A001333(n+1) + 1. - Sean A. Irvine, Aug 23 2024

Extensions

An incorrect recurrence was deleted by N. J. A. Sloane, Sep 13 2009
More terms from Sean A. Irvine, Aug 23 2024

A069441 Half the number of n X 3 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

Original entry on oeis.org

0, 4, 84, 1074, 11058, 102448, 896026, 7578952, 62820362, 514178822, 4174954460, 33725176208, 271523097884, 2181288088576, 17498432045552, 140241880816930, 1123280018219562, 8993350007112124, 71984384316723134, 576073752326317448, 4609640266662591130
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

Formula

a(n) = 2^(3*n-1) - A069378(n) + A069403(n). - Sean A. Irvine, Aug 23 2024

Extensions

More terms from Sean A. Irvine, Aug 23 2024

A069442 Half the number of n X 4 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

Original entry on oeis.org

0, 8, 440, 13002, 291782, 5718464, 103948054, 1806753034, 30539121806, 507006229578, 8318320069722, 135401306105052, 2192221953687972, 35363748022460400, 569037825802441810, 9140526218802015968, 146649357444276412850, 2350864549078452042124
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

Formula

a(n) = 2^(4*n-1) - A069379(n) + A069404(n). - Sean A. Irvine, Aug 23 2024

Extensions

More terms from Sean A. Irvine, Aug 23 2024

A069443 Half the number of n X 5 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

Original entry on oeis.org

0, 16, 2304, 157058, 7664414, 317229344, 11974298030, 427585649578, 14741384488782, 496652156206058, 16475668543000750, 540790107010874580, 17620412998483400934, 571161367966749399684, 18446500586660704024820, 594209705207122247276746
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

Formula

a(n) = 2^(5*n-1) - A069380(n) + A069405(n). - Sean A. Irvine, Aug 23 2024

Extensions

More terms from Sean A. Irvine, Aug 23 2024

A069444 Half the number of n X 6 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

Original entry on oeis.org

32, 12064, 1896074, 200993408, 17550580192, 1374566625956
Offset: 2

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069445 Half the number of n X 7 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

Original entry on oeis.org

64, 63168, 22886754, 5267756806
Offset: 2

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069446 Half the number of n X 8 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

Original entry on oeis.org

128, 330752, 276246170, 138031237058
Offset: 2

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069449 Half the number of 4 X n binary arrays with no path of adjacent 1's or adjacent 0's from top to bottom or side to side.

Original entry on oeis.org

7, 269, 5799, 95783, 1389619, 18772467, 243194821, 3070812013
Offset: 2

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069450 Half the number of 5 X n binary arrays with no path of adjacent 1's or adjacent 0's from top to bottom or side to side.

Original entry on oeis.org

15, 1723, 95783, 3802615, 127780201, 3912171001
Offset: 2

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A000225, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.
Previous Showing 81-90 of 91 results. Next

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