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.

Previous Showing 21-30 of 93 results. Next

A069382 Number of n X 7 binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

127, 14197, 1461797, 144769425, 14142942975, 1374273318721, 133267613878665, 12913642307413193, 1251002814214706415, 121180225103268487525, 11738064445690843712709, 1137001292953873957167377, 110135446775389136829629647, 10668293121854243285020490369
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Links

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

More terms from Sean A. Irvine, Apr 30 2024

A069383 Number of n X 8 binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

255, 58975, 12519345, 2541013617, 506544513343, 100193001007135, 19752116290408897, 3888492110032895921, 765068584835726823447, 150495460332124702700743, 29601436900513534956486417, 5822276945638780019957186657, 1145175890285973091225709069559
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Links

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

More terms from Sean A. Irvine, Apr 30 2024

A069384 Number of n X 9 binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

511, 242461, 105683341, 43843180113, 17792504911231, 7146486319870849, 2856738227918860537, 1139431807812280823353, 454016084146597129480639, 180827014727915133583355805, 72007238386097441302774324845, 28672084199736350940864453233905
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Links

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

More terms from Sean A. Irvine, Apr 30 2024

A069385 Number of n X 10 binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1023, 989527, 882516857, 746691527217, 615793150236223, 501394148790682463, 405671453894948801169, 327195886636045773364289, 263496356226918378172858791, 212041997127527144580159558415, 170577316159214009818521435822905, 137200626549758017615769211506956897
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Links

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

More terms from Sean A. Irvine, Apr 30 2024

A069386 Number of n X 11 binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

2047, 4017157, 7308428597, 12588144461329, 21067276157958271, 34728307983514473409, 56797093221062281961353, 92506527736225809457497129, 150343681421865609328377897039, 244072929303780515911965529991989, 396017759826921556057184566557279157
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Links

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

More terms from Sean A. Irvine, Apr 30 2024

A069387 Number of n X 12 binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

4095, 16245775, 60131384705, 210502738714097, 714097521397778495, 2380826437768134741023, 7862987107940658832635809, 25834416752721407468468718385, 84641600245355780352751022513463, 276889755885138056467643815501003447, 905061607197623234620822097612564300097
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Links

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

More terms from Sean A. Irvine, Apr 30 2024

A369892 Array read by antidiagonals: T(m, n) is the number of m X n binary arrays with a path of adjacent 1's from top row to bottom row using only left, right, and downward steps.

Original entry on oeis.org

1, 3, 1, 7, 7, 1, 15, 37, 17, 1, 31, 175, 197, 41, 1, 63, 781, 1985, 1041, 99, 1, 127, 3367, 18621, 22193, 5503, 239, 1, 255, 14197, 167337, 433801, 247759, 29089, 577, 1, 511, 58975, 1461797, 8057625, 10056087, 2764991, 153769, 1393, 1, 1023, 242461, 12519345, 144762849, 384409519, 232777209, 30856705, 812849, 3363, 1
Offset: 1

Views

Author

Caleb Stanford, Feb 05 2024

Keywords

Comments

Similar to A359576 but disallowing Up steps.
The sequences are initially similar but differ for 4 X 5 grids (433801 instead of 433809), 4 X 6 grids (8057625 instead of 8057905), and 5 X 5 grids (10056087 instead of 10056959)
Can be calculated by dynamic programming from 1 X n grids to m X n grids by keeping track of the number of grids with each of the 2^n patterns of reachable squares in the last row.
Each row and each column satisfies a linear recurrence with constant coefficients. - Pontus von Brömssen, Feb 05 2025

Examples

			For the 37 2 X 3 grids, see A359576.
The following 4 X 5 grid is a counterexample that is counted by A359576 but not by the present sequence:
    10000
    10111
    11101
    00001
Notice that there is a path of 1s from the top to the bottom, but only via the upward step detour in the third column. There are 8 such 4 X 5 grids, formed from the above by reflection and by toggling the first row, second column and last row, second to last column.
Table starts:
    1      3        7         15          31          63         127 ...
    1      7       37        175         781        3367       14197 ...
    1     17      197       1985       18621      167337     1461797 ...
    1     41     1041      22193      433801     8057625   144762849 ...
    1     99     5503     247759    10056087   384409519   ...
    1    239    29089    2764991   232777209   ...
    1    577   153769   30856705   ...
    1   1393   812849   ...
    1   3363   ...
    1   ...
    ...

Links

Crossrefs

First 4 rows are A000225, A005061, A069361, A368809.
First 4 columns are A000012, A001333, A069378, A069379.
Cf. A359576 (up steps allowed).

A069364 Number of 6 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 239, 29089, 2764991, 232824241, 18287614751, 1374273318721, 100193001007135, 7146486319870849, 501394148790682463, 34728307983514473409, 2380826437768134741023, 161857825276476548906497
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

a(9)-a(13) from Sean A. Irvine, Apr 29 2024

A069365 Number of 7 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 577, 153769, 30856705, 5388274121, 868972410929, 133267613878665, 19752116290408897, 2856738227918860537, 405671453894948801169, 56797093221062281961353, 7862987107940658832635809, 1078636993747832299068001753
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

a(7)-a(13) from Sean A. Irvine, Apr 29 2024

A069366 Number of 8 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 1393, 812849, 344356289, 124693133113, 41278350729313, 12913642307413193, 3888492110032895921, 1139431807812280823353, 327195886636045773364289, 92506527736225809457497129, 25834416752721407468468718385, 7143459701634079128687197933529
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2002

Keywords

Crossrefs

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Extensions

a(7)-a(13) from Sean A. Irvine, Apr 29 2024
Previous Showing 21-30 of 93 results. Next

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

Content is available under The OEIS End-User License Agreement.