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 11-20 of 20 results.

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

A155602 4^n + 3^n - 1.

Original entry on oeis.org

1, 6, 24, 90, 336, 1266, 4824, 18570, 72096, 281826, 1107624, 4371450, 17308656, 68703186, 273218424, 1088090730, 4338014016, 17309009346, 69106897224, 276040168410, 1102998412176, 4408506864306, 17623567104024, 70462887356490
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592-A155594, A155596-A155601.

Programs

Formula

G.f.: 1/(1-4*x)+1/(1-3*x)-1/(1-x). E.g.f.: e^(4*x)+e^(3*x)-e^x.
a(n) = 7*a(n-1) - 12*a(n-2) -6, n>1 - Gary Detlefs, Jun 21 2010
a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3), n>2, a(0)=1, a(1)=6, a(2)=24. - L. Edson Jeffery, Oct 17 2012
a(n) = A074605(n)-1. - R. J. Mathar, Mar 10 2022

A155603 a(n) = 5^n+3^n-1.

Original entry on oeis.org

1, 7, 33, 151, 705, 3367, 16353, 80311, 397185, 1972807, 9824673, 49005271, 244672065, 1222297447, 6108298593, 30531927031, 152630937345, 763068593287, 3815084686113, 19074648589591, 95370918425025, 476847618556327
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602.

Programs

Formula

G.f.: 1/(1-5*x)+1/(1-3*x)-1/(1-x).
E.g.f.: e^(5*x)+e^(3*x)-e^x.
a(n) = 8*a(n-1)-15*a(n-2)-8 with a(0)=1, a(1)=7. - Vincenzo Librandi, Jul 21 2010
a(n) = A074606(n)-1. - R. J. Mathar, Mar 10 2022

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

A155604 a(n) = 6^n + 3^n - 1.

Original entry on oeis.org

1, 8, 44, 242, 1376, 8018, 47384, 282122, 1686176, 10097378, 60525224, 362974202, 2177313776, 13062288338, 78368947064, 470199333482, 2821152954176, 16926788584898, 101560344088904, 609360902271962, 3656161926847376
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603.

Programs

Formula

G.f.: 1/(1-6*x)+1/(1-3*x)-1/(1-x).
E.g.f.: exp(6*x)+exp(3*x)-exp(x).
a(n) = 9*a(n-1)-18*a(n-2)-10 with a(0) = 1, a(1) = 8. - Vincenzo Librandi, Jul 21 2010

A155605 7^n+3^n-1.

Original entry on oeis.org

1, 9, 57, 369, 2481, 17049, 118377, 825729, 5771361, 40373289, 282534297, 1977503889, 13841818641, 96890604729, 678227855817, 4747575858849, 33232973616321, 232630643127369, 1628413985330937, 11398896347634609
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604.

Programs

Formula

G.f.: 1/(1-7*x)+1/(1-3*x)-1/(1-x). E.g.f.: e^(7*x)+e^(3*x)-e^x.
a(n)=10*a(n-1)-21*a(n-2)-12 with a(0)=1, a(1)=9 - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=9, a(2)=57, a(n)=11*a(n-1)-31*a(n-2)+21*a(n-3). - Harvey P. Dale, Nov 09 2012

A155606 a(n) = 8^n + 3^n - 1.

Original entry on oeis.org

1, 10, 72, 538, 4176, 33010, 262872, 2099338, 16783776, 134237410, 1073800872, 8590111738, 68720008176, 549757408210, 4398051294072, 35184386437738, 281475019757376, 2251799942825410, 18014398896902472, 144115189238117338
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Examples

			G.f. = 1 + 10*x + 72*x^2 + 538*x^3 + 4176*x^4 + 33010*x^5 + 262872*x^6 + ...

Links

Crossrefs

Cf. A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605.

Programs

Formula

G.f.: 1/(1-8*x) + 1/(1-3*x) - 1/(1-x).
E.g.f.: e^(8*x) + e^(3*x) - e^x.
a(n) = 11*a(n-1) - 24*a(n-2) - 14 with a(0)=1, a(1)=10. - Vincenzo Librandi, Jul 21 2010

A155595 11^n+2^n-1.

Original entry on oeis.org

1, 12, 124, 1338, 14656, 161082, 1771624, 19487298, 214359136, 2357948202, 25937425624, 285311672658, 3138428380816, 34522712152122, 379749833599624, 4177248169448418, 45949729863637696, 505447028499424842
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 24 2009

Keywords

Links

Crossrefs

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590, A155592, A155593, A155594.

Programs

Formula

G.f.: 1/(1-11*x)+1/(1-2*x)-1/(1-x). E.g.f.: e^(11*x)+e^(2*x)-e^x.
a(n)=13*a(n-1)-22*a(n-2)-10 with a(0)=1, a(1)=12 - Vincenzo Librandi, Jul 21 2010
Previous Showing 11-20 of 20 results.

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