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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A069425 Number of n X 5 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 211, 9539, 300651, 8168645, 206458895, 5022868187, 119647195507, 2816023729437, 65818825735031, 1532136293558119, 35579894275049831, 825082170362304285, 19117256012937548815, 442728846445605819023, 10249950234312030878755, 237262687880593853560805
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A001047, n X 2 A034182, 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) = A069380(n) - 2 * A069405(n). - Sean A. Irvine, Aug 23 2024

Extensions

More terms from Sean A. Irvine, Aug 23 2024

A069426 Number of n X 6 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 665, 70679, 4927163, 287275073
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A001047, n X 2 A034182, 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.

A069427 Number of n X 7 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 2059, 509019, 77892523, 9681281781
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 2 X n A001047, n X 2 A034182, 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.

A069430 Half the number of 4 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

7, 88, 1074, 13002, 157058, 1896074, 22886754, 276246170, 3334295986, 40244915946, 485755429442, 5863058792506, 70767006224978, 854156391897098, 10309651065637602, 124437288171423322
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

Empirical (for n>=6): a(n) = 19*a(n-1) - 98*a(n-2) + 180*a(n-3) - 80*a(n-4) - 16*a(n-5). - Vaclav Kotesovec, Nov 28 2012
Empirical g.f.: x*(7 - 45*x + 88*x^2 - 40*x^3 - 8*x^4) / (1 - 19*x + 98*x^2 - 180*x^3 + 80*x^4 + 16*x^5). - Colin Barker, Oct 12 2017

A069431 Half the number of 5 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

15, 414, 11058, 291782, 7664414, 200993408, 5267756806, 138031237058, 3616567402784
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.

A069432 Half the number of 6 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

31, 1810, 102448, 5718464, 317229344, 17550580192
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.

A069433 Half the number of 7 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

63, 7616, 896026, 103948054, 11974298030, 1374566625956
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.

A069434 Half the number of 8 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

127, 31376, 7578952, 1806753034, 427585649578
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.

A069435 Half the number of 9 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

255, 127710, 62820362, 30539121806, 14741384488782
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.

A069436 Half the number of 10 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

511, 516170, 514178822, 507006229578
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.
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