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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A061252 a(n) = 16^n - 15^n.

Original entry on oeis.org

0, 1, 31, 721, 14911, 289201, 5386591, 97576081, 1732076671, 30276117361, 522861237151, 8942430185041, 151728638820031, 2557404559011121, 42864668012537311, 715027614225987601, 11878335717996660991
Offset: 0

Views

Author

Frank Ellermann, Jun 05 2001

Keywords

Comments

Number of ways to assign truth values to n quaternary conjunctions connected by disjunctions such that the proposition is true. For example, a(2) = 31, since for the proposition '(a & b & c & d) v (e & f & g & h)' there are 31 assignments that make the proposition true. - Ori Milstein, Dec 31 2022
Equivalently, the number of length-n words over the alphabet {0,1,..,15} with at least one letter = 15. - Joerg Arndt, Jan 01 2023

Links

Crossrefs

Base 8: A016177, 4: A005061, 2: A000225, 10: A016189.

Programs

  • Mathematica
    Table[16^n-15^n,{n,0,20}] (* or  *) LinearRecurrence[{31,-240},{0,1},20] (* Harvey P. Dale, Jan 23 2021 *)
  • PARI
    a(n) = 16^n - 15^n; \\ Michel Marcus, Aug 26 2013

Formula

a(0)=0, a(n) = 15*a(n-1) + 16^(n-1). - Vincenzo Librandi, Feb 09 2011
a(0)=0, a(1)=1, a(n) = 31*a(n-1) - 240*a(n-2). - Vincenzo Librandi, Feb 09 2011
a(n) = A001025(n) - A001024(n). - Michel Marcus, Aug 26 2013

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

A069367 Number of 9 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 3363, 4296863, 3842988975, 2885579381831, 1960665141991079, 1251002814214706415, 765068584835726823447, 454016084146597129480639, 263496356226918378172858791, 150343681421865609328377897039, 84641600245355780352751022513463, 47141832001173360326967315743610399
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

A069368 Number of 10 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 8119, 22713981, 42887577455, 66776768695477, 93127506982471999, 121180225103268487525, 150495460332124702700743, 180827014727915133583355805, 212041997127527144580159558415, 244072929303780515911965529991989, 276889755885138056467643815501003447
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(6)-a(12) from Sean A. Irvine, Apr 29 2024

A069369 Number of 11 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 19601, 120070149, 478623939553, 1545323639404349, 4423369428678533705, 11738064445690843712709, 29601436900513534956486417, 72007238386097441302774324845, 170577316159214009818521435822905, 396017759826921556057184566557279157
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(6)-a(11) from Sean A. Irvine, Apr 30 2024

A069370 Number of 12 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 47321, 634712209, 5341429762353, 35761396310047985, 210101996822111263265, 1137001292953873957167377, 5822276945638780019957186657, 28672084199736350940864453233905, 137200626549758017615769211506956897, 642383534197189939475136495116939323825
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(6)-a(11) from Sean A. Irvine, Apr 30 2024

A069371 Number of 13 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 114243, 3355201895, 59610217019311, 827579980089997079, 9979493366382754619551, 110135446775389136829629647, 1145175890285973091225709069559, 11416514838646336435351220608498495, 110348288974297906676696735021969395495
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(6)-a(10) from Sean A. Irvine, Apr 30 2024

A069372 Number of 14 X n binary arrays with a path of adjacent 1's from top row to bottom row.

Original entry on oeis.org

1, 275807, 17736195433, 665248512113343, 19151628770974955241, 474010149850018604630031, 10668293121854243285020490369, 225244010686408578974151583689991, 4545766298041234760046713199408324081, 88749814849001992025685589472619159396919
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(6)-a(10) from Sean A. Irvine, Apr 30 2024
Previous Showing 61-70 of 84 results. Next

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