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 1-7 of 7 results.

A155614 9^n - 3^n + 1.

Original entry on oeis.org

1, 7, 73, 703, 6481, 58807, 530713, 4780783, 43040161, 387400807, 3486725353, 31380882463, 282429005041, 2541864234007, 22876787671993, 205891117745743, 1853020145805121, 16677181570526407, 150094634909578633
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

Links

Crossrefs

Cf. A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612, A155613.

Programs

Formula

G.f.: 1/(1-9*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(9*x)-e^(3*x)+e^x.
a(n) = 12*a(n-1)-27*a(n-2)+16 with a(0)=1, a(1)=7. - Vincenzo Librandi, Jul 21 2010

A155615 a(n) = 10^n - 3^n + 1.

Original entry on oeis.org

1, 8, 92, 974, 9920, 99758, 999272, 9997814, 99993440, 999980318, 9999940952, 99999822854, 999999468560, 9999998405678, 99999995217032, 999999985651094, 9999999956953280, 99999999870859838, 999999999612579512
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

Links

Crossrefs

Cf. A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614.

Programs

Formula

G.f.: 1/(1-10*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(10*x)-e^(3*x)+e^x.
a(n) = 13*a(n-1)-30*a(n-2)+18 with a(0)=1, a(1)=8. - Vincenzo Librandi, Jul 21 2010

A155616 5^n + 4^n - 1.

Original entry on oeis.org

1, 8, 40, 188, 880, 4148, 19720, 94508, 456160, 2215268, 10814200, 53022428, 260917840, 1287811988, 6371951080, 31591319948, 156882857920, 780119322308, 3883416742360, 19348364235068, 96466943268400, 481235204714228
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 27 2009

Keywords

Links

Crossrefs

Cf. A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615.

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)=8 - Vincenzo Librandi, Jul 21 2010

A155617 a(n) = 6^n + 4^n - 1.

Original entry on oeis.org

1, 9, 51, 279, 1551, 8799, 50751, 296319, 1745151, 10339839, 61514751, 366991359, 2193559551, 13127802879, 78632599551, 471258726399, 2825404874751, 16943839313919, 101628676145151, 609634617917439, 3657257951690751
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 27 2009

Keywords

Links

Crossrefs

Cf. A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616.

Programs

Formula

G.f.: 1/(1-6*x)+1/(1-4*x)-1/(1-x).
E.g.f.: exp(6*x) + exp(4*x) - exp(x).
a(n) = 10*a(n-1)-24*a(n-2) -15, n>1 - Gary Detlefs, Jun 21 2010
a(n) = 11*a(n-1)-34*a(n-2)+24*a(n-3). - Vincenzo Librandi, Feb 16 2013

A155618 a(n) = 7^n+4^n-1^n.

Original entry on oeis.org

1, 10, 64, 406, 2656, 17830, 121744, 839926, 5830336, 40615750, 283523824, 1981521046, 13858064416, 96956119270, 678491508304, 4748635251766, 33237225536896, 232647693856390, 1628482317387184, 11399170063280086
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 27 2009

Keywords

Links

Crossrefs

A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616, A155617

Programs

Formula

G.f.: 1/(1-7*x)+1/(1-4*x)-1/(1-x). E.g.f.: e^(7*x)+e^(4*x)-e^x.
a(n) = 11*a(n-1)-28*a(n-2)-18 with a(0)=1, a(1)=10 [Vincenzo Librandi, Jul 21 2010]
a(0)=1, a(1)=10, a(2)=64, a(n) = 12*a(n-1)-39*a(n-2)+28*a(n-3). - Harvey P. Dale, Feb 04 2014

A155619 8^n+4^n-1^n.

Original entry on oeis.org

1, 11, 79, 575, 4351, 33791, 266239, 2113535, 16842751, 134479871, 1074790399, 8594128895, 68736253951, 549822922751, 4398314946559, 35185445830655, 281479271677951, 2251816993554431, 18014467228958719, 144115462953762815
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 27 2009

Keywords

Links

Crossrefs

A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616, A155617, A155618

Programs

  • Mathematica
    Table[8^n+4^n-1,{n,0,30}] (* or *) LinearRecurrence[{13,-44,32},{1,11,79},30] (* Harvey P. Dale, Jun 19 2013 *)

Formula

G.f.: 1/(1-8*x)+1/(1-4*x)-1/(1-x). E.g.f.: e^(8*x)+e^(4*x)-e^x.
a(n)=12*a(n-1)-32*a(n-2)-21 with a(0)=1, a(1)=11 [From Vincenzo Librandi, Jul 21 2010]
a(0)=1, a(1)=11, a(2)=79, a(n)=13*a(n-1)-44*a(n-2)+32*a(n-3). - Harvey P. Dale, Jun 19 2013

A155621 10^n+4^n-1^n.

Original entry on oeis.org

1, 13, 115, 1063, 10255, 101023, 1004095, 10016383, 100065535, 1000262143, 10001048575, 100004194303, 1000016777215, 10000067108863, 100000268435455, 1000001073741823, 10000004294967295, 100000017179869183
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 27 2009

Keywords

Links

Crossrefs

A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616, A155617, A155618, A155619, A155620

Programs

  • Mathematica
    LinearRecurrence[{15,-54,40},{1,13,115},20] (* Harvey P. Dale, Oct 24 2016 *)

Formula

G.f.: 1/(1-10*x)+1/(1-4*x)-1/(1-x). E.g.f.: e^(10*x)+e^(4*x)-e^x.
a(n)=14*a(n-1)-40*a(n-2)-27 with a(0)=1, a(1)=13 [From Vincenzo Librandi, Jul 21 2010]
Showing 1-7 of 7 results.

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

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