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 1-5 of 5 results.

A155624 11^n-3^n+1.

Original entry on oeis.org

1, 9, 113, 1305, 14561, 160809, 1770833, 19484985, 214352321, 2357928009, 25937365553, 285311493465, 3138427845281, 34522710549609, 379749828800273, 4177248155066745, 45949729820525441, 505447028370153609
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 29 2009

Keywords

Links

Crossrefs

Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623.

Programs

Formula

G.f.: 1/(1-11*x)-1/(1-3*x)+1/(1-x). E.g.f.: e^(11*x)-e^(3*x)+e^x.
a(n)=14*a(n-1)-33*a(n-2)+20 with a(0)=1, a(1)=9 - Vincenzo Librandi, Jul 21 2010

A155625 a(n) = 11^n + 4^n - 1.

Original entry on oeis.org

1, 14, 136, 1394, 14896, 162074, 1775656, 19503554, 214424416, 2358209834, 25938473176, 285315864914, 3138445153936, 34522779252794, 379750102018696, 4177249243157474, 45949734158539456, 505447045679162954, 5559917382211708216, 61159090723292453234, 672749996032071636976
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 29 2009

Keywords

Links

Crossrefs

Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624.

Programs

Formula

G.f.: 1/(1-11*x)+1/(1-4*x)-1/(1-x).
E.g.f.: exp(11*x)+exp(4*x)-exp(x).
a(n) = 15*a(n-1)-44*a(n-2)-30 with a(0) = 1, a(1) = 14. - Vincenzo Librandi, Jul 21 2010

A155626 a(n) = 5^n-4^n+1.

Original entry on oeis.org

1, 2, 10, 62, 370, 2102, 11530, 61742, 325090, 1690982, 8717050, 44633822, 227363410, 1153594262, 5835080170, 29443836302, 148292923330, 745759583942, 3745977788890, 18798608421182, 94267920012850, 472439111692022
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 29 2009

Keywords

Links

Crossrefs

Cf. A054401, which is essentially a(n) - 2. Also A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625.

Programs

Formula

G.f.: 1/(1-5*x)-1/(1-4*x)+1/(1-x).
E.g.f.: e^(5*x)-e^(4*x)+e^x.
a(n) = 9*a(n-1)-20*a(n-2)+12 with a(0)=1, a(1)=2. - Vincenzo Librandi, Jul 21 2010
a(n) = 10*a(n-1)-29*a(n-2)+20*a(n-3). - Wesley Ivan Hurt, Jun 07 2021

A155623 a(n) = 11^n + 3^n - 1.

Original entry on oeis.org

1, 13, 129, 1357, 14721, 161293, 1772289, 19489357, 214365441, 2357967373, 25937483649, 285311847757, 3138428908161, 34522713738253, 379749838366209, 4177248183764557, 45949729906618881, 505447028628433933
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 29 2009

Keywords

Comments

a^n+b^n-1^n=(a+b)*a(n-1)-(a*b)*a(n-2)-(a-1)*(b-1) - Vincenzo Librandi, Jul 21 2010

Links

Crossrefs

Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622.

Programs

Formula

G.f.: 1/(1 - 11*x) + 1/(1 - 3*x) - 1/(1 - x).
E.g.f.: exp(11*x) + exp(3*x) - exp(x).
a(n) = 14*a(n-1) - 33*a(n-2) - 20 for n>1, a(0)=1, a(1)=13 - Vincenzo Librandi, Jul 21 2010

A155622 a(n) = 11^n - 2^n + 1.

Original entry on oeis.org

1, 10, 118, 1324, 14626, 161020, 1771498, 19487044, 214358626, 2357947180, 25937423578, 285311668564, 3138428372626, 34522712135740, 379749833566858, 4177248169382884, 45949729863506626, 505447028499162700
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 29 2009

Keywords

Comments

In general: r^n - s^n + 1 = (r+s)*a(n-1)-(r*s)*a(n-2)+(r-1)*(s-1). - Vincenzo Librandi, Jul 21 2010

Links

Crossrefs

Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601.

Programs

  • Mathematica
    Table[11^n - 2^n + 1, {n, 0, 20}] (* or *) LinearRecurrence[{14, -35, 22}, {1, 10, 118}, 20] (* Harvey P. Dale, Oct 21 2013 *)
  • PARI
    a(n)=11^n-2^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1 - 11*x) - 1/(1 - 2*x) + 1/(1-x).
E.g.f.: exp(11*x) - exp(2*x) + exp(x).
a(n) = 13*a(n-1) - 22*a(n-2) + 10 for n>1, a(0)=1, a(1)=10. - Vincenzo Librandi, Jul 21 2010
Showing 1-5 of 5 results.

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