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 1-9 of 9 results.

A121213 a(n) = 7^n - 5^n.

Original entry on oeis.org

0, 2, 24, 218, 1776, 13682, 102024, 745418, 5374176, 38400482, 272709624, 1928498618, 13597146576, 95668307282, 672119557224, 4717043931818, 33080342678976, 231867574534082, 1624598900644824, 11379821699045018
Offset: 0

Views

Author

Mohammad K. Azarian, Aug 19 2006

Keywords

Links

Crossrefs

Cf. A074616, A081200.

Programs

Formula

a(n) = 12*a(n-1) - 35*a(n-2) with a(0)=0, a(1)=2. - Vincenzo Librandi, Jul 21 2010
a(n) = 2*A081200(n). - Reinhard Zumkeller, Aug 01 2010
G.f.: 2*x/((5*x-1)*(7*x-1)). - Colin Barker, Nov 05 2012
E.g.f.: 2*exp(6*x)*sinh(x). - Elmo R. Oliveira, Mar 31 2025

A245807 a(n) = 7^n + 10^n.

Original entry on oeis.org

2, 17, 149, 1343, 12401, 116807, 1117649, 10823543, 105764801, 1040353607, 10282475249, 101977326743, 1013841287201, 10096889010407, 100678223072849, 1004747561509943, 10033232930569601, 100232630513987207, 1001628413597910449, 10011398895185373143
Offset: 0

Views

Author

Vincenzo Librandi, Aug 04 2014

Keywords

Links

Crossrefs

Cf. 7^n+k^n: A034491 (k=1), A074602 (k=2), A074608 (k=3), A074613 (k=4), A074616 (k=5), A074619 (k=6), A109808 (k=7), A074622 (k=8), A074623 (k=9), this sequence (k=10).

Programs

  • Magma
    [7^n+10^n: n in [0..25]];
  • Magma
    I:=[2,17]; [n le 2 select I[n] else 17*Self(n-1)-70*Self(n-2): n in [1..25]];
  • Mathematica
    Table[(7^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 17 x)/((1 - 7 x) (1 - 10 x)), {x, 0, 40}], x]

Formula

G.f.: (2-17*x)/((1-7*x)*(1-10*x)).
E.g.f.: e^(7*x) + e^(10*x).
a(n) = 17*a(n-1)-70*a(n-2).
a(n) = A000420(n) + A011557(n).

A045596 Numbers k that divide 7^k + 5^k.

Original entry on oeis.org

1, 2, 3, 9, 27, 39, 74, 81, 117, 243, 351, 507, 729, 1053, 1521, 2187, 2738, 3081, 3159, 4563, 6123, 6561, 6591, 9243, 9477, 12207, 13689, 18369, 19683, 19773, 27729, 28431, 36621, 40053, 41067, 43882, 55107, 59049, 59319, 79599, 83187, 85293
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A074616.

Programs

  • Mathematica
    Select[Range[86000],Mod[PowerMod[7,#,#]+PowerMod[5,#,#],#]==0&] (* Harvey P. Dale, Aug 02 2023 *)

A121199 12n+7^n+5^n.

Original entry on oeis.org

2, 24, 98, 504, 3074, 19992, 133346, 901752, 6155522, 42306840, 292240994, 2026155000, 14085427970, 98109713688, 684326588642, 4778079088248, 33385518460418, 233393453440536, 1632228295176290, 11417968671701496
Offset: 0

Views

Author

Mohammad K. Azarian, Aug 19 2006

Keywords

Links

Crossrefs

Cf. A074616.

Programs

  • Magma
    [12*n+7^n+5^n: n in [0..20]]; // Bruno Berselli, Feb 27 2013
  • Mathematica
    CoefficientList[Series[2 (1 - 2 x - 59 x^2 + 204 x^3)/((1-x)^2 (1-7 x) (1-5 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Feb 23 2013 *)
Table[12 n + 7^n + 5^n, {n, 0, 20}] (* Bruno Berselli, Feb 27 2013 *)
LinearRecurrence[{14,-60,82,-35},{2,24,98,504},20] (* Harvey P. Dale, Aug 15 2013 *)
  • PARI
    for(n=0, 20, print1(12*n+7^n+5^n", ")); \\ Bruno Berselli, Feb 27 2013

Formula

G.f.: 2*(1-2*x-59*x^2+204*x^3)/((1-x)^2*(1-7*x)*(1-5*x)). - Vincenzo Librandi, Feb 23 2013

Extensions

Edited by Ray Chandler, Sep 06 2006

A121200 a(n) = 2*n + 7^n + 5^n.

Original entry on oeis.org

2, 14, 78, 474, 3034, 19942, 133286, 901682, 6155442, 42306750, 292240894, 2026154890, 14085427850, 98109713558, 684326588502, 4778079088098, 33385518460258, 233393453440366, 1632228295176110, 11417968671701306
Offset: 0

Views

Author

Mohammad K. Azarian, Aug 19 2006

Keywords

Links

Crossrefs

Cf. A074616.

Programs

  • Magma
    [2*n+7^n+5^n: n in [0..30]]; // Vincenzo Librandi, Feb 25 2013
  • Mathematica
    Table[2 n + 7^n + 5^n, {n, 0, 20}]  (* Harvey P. Dale, Mar 30 2011 *)
CoefficientList[Series[2 (1 - 7 x + x^2 + 29 x^3)/((1 - x)^2 (1 - 5 x)(1 - 7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 25 2013 *)

Formula

G.f.: 2*(1-7*x+x^2+29*x^3)/((1-x)^2*(1-5*x)*(1-7*x)). - Vincenzo Librandi, Feb 25 2013

Extensions

Edited by Ray Chandler, Sep 06 2006

A121201 a(n) = 7^n+5^n-2n.

Original entry on oeis.org

2, 10, 70, 462, 3018, 19922, 133262, 901654, 6155410, 42306714, 292240854, 2026154846, 14085427802, 98109713506, 684326588446, 4778079088038, 33385518460194, 233393453440298, 1632228295176038, 11417968671701230
Offset: 0

Views

Author

Mohammad K. Azarian, Aug 19 2006

Keywords

Links

Crossrefs

Cf. A074616.

Programs

  • Magma
    [7^n+5^n-2*n: n in [0..20]]; // Vincenzo Librandi, Feb 25 2013
  • Magma
    I:=[2,10,70,462]; [n le 4 select I[n] else 14*Self(n-1)-60*Self(n-2)+82*Self(n-3)-35*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 25 2013
  • Mathematica
    CoefficientList[Series[2 (1 - 9 x + 25 x^2 - 41 x^3)/((1-x)^2 (1-5 x)(1-7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 25 2013 *)
LinearRecurrence[{14,-60,82,-35},{2,10,70,462},30] (* Harvey P. Dale, Dec 21 2014 *)

Formula

G.f.: 2*(1-9*x+25*x^2-41*x^3)/((1-x)^2*(1-5*x)*(1-7*x)). - Vincenzo Librandi, Feb 25 2013
a(n) = 14*a(n-1)-60*a(n-2)+82*a(n-3)-35*a(n-4). - Vincenzo Librandi, Feb 26 2013

Extensions

Edited by Ray Chandler, Sep 06 2006

A121202 a(n) = 12*n + 7^n - 5^n.

Original entry on oeis.org

0, 14, 48, 254, 1824, 13742, 102096, 745502, 5374272, 38400590, 272709744, 1928498750, 13597146720, 95668307438, 672119557392, 4717043931998, 33080342679168, 231867574534286, 1624598900645040, 11379821699045246
Offset: 0

Views

Author

Mohammad K. Azarian, Aug 19 2006

Keywords

Links

Crossrefs

Cf. A074616.

Programs

  • Magma
    [7^n - 5^n + 12*n: n in [0..30]]; // Vincenzo Librandi, Feb 25 2013
  • Magma
    I:=[0, 14, 48, 254]; [n le 4 select I[n] else 14*Self(n-1)-60*Self(n-2)+82*Self(n-3)-35*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 25 2013
  • Mathematica
    CoefficientList[Series[2 (7 x - 74 x^2 + 211 x^3)/((1-x)^2 (1-5 x)(1-7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 25 2013 *)

Formula

G.f.: 2*(7*x-74*x^2+211*x^3)/((1-x)^2*(1-5*x)*(1-7*x)). - Vincenzo Librandi, Feb 25 2013
a(n) = 14*a(n-1)-60*a(n-2)+82*a(n-3)-35*a(n-4). - Vincenzo Librandi, Feb 27 2013

Extensions

Edited by Ray Chandler, Sep 06 2006

A121203 a(n) = 2n+7^n-5^n.

Original entry on oeis.org

0, 4, 28, 224, 1784, 13692, 102036, 745432, 5374192, 38400500, 272709644, 1928498640, 13597146600, 95668307308, 672119557252, 4717043931848, 33080342679008, 231867574534116, 1624598900644860, 11379821699045056
Offset: 0

Views

Author

Mohammad K. Azarian, Aug 19 2006

Keywords

Links

Crossrefs

Cf. A074616.

Programs

  • Magma
    [2*n+7^n-5^n: n in [0..30]]; // Vincenzo Librandi, Feb 26 2013
  • Magma
    I:=[0,4,28,224]; [n le 4 select I[n] else 14*Self(n-1)-60*Self(n-2)+82*Self(n-3)-35*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 26 2013
  • Mathematica
    CoefficientList[Series[4 x (1 - 7 x + 18 x^2)/((1-x)^2 (1-5 x)(1-7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 25 2013 *)

Formula

G.f.: 4*x*(1-7*x+18*x^2)/((1-x)^2*(1-5*x)*(1-7*x)). - Vincenzo Librandi, Feb 25 2013
a(n) = 14*a(n-1)-60*a(n-2)+82*a(n-3)-35*a(n-4). - Vincenzo Librandi, Feb 26 2013

Extensions

Edited by Ray Chandler, Sep 06 2006

A121204 -2n+7^n-5^n.

Original entry on oeis.org

0, 0, 20, 212, 1768, 13672, 102012, 745404, 5374160, 38400464, 272709604, 1928498596, 13597146552, 95668307256, 672119557196, 4717043931788, 33080342678944, 231867574534048, 1624598900644788, 11379821699044980
Offset: 0

Views

Author

Mohammad K. Azarian, Aug 19 2006

Keywords

Links

Crossrefs

Cf. A074616.

Programs

  • Magma
    I:=[0, 0, 20, 212]; [n le 4 select I[n] else 14*Self(n-1)-60*Self(n-2)+82*Self(n-3)-35*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 26 2013
  • Mathematica
    CoefficientList[Series[4 x^2 (5 - 17 x)/((1 - x)^2 (1 - 5 x)(1 - 7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 26 2013 *)
LinearRecurrence[{14,-60,82,-35},{0,0,20,212},20] (* Harvey P. Dale, Nov 30 2022 *)

Formula

G.f.: 4*x^2*(5-17*x)/((1-x)^2 (1-5*x)(1-7*x)). - Vincenzo Librandi. Feb 26 2013
a(n) = 14*a(n-1)-60*a(n-2)+82*a(n-3)-35*a(n-4). - Vincenzo Librandi, Feb 26 2013

Extensions

Edited by Ray Chandler, Sep 06 2006
Showing 1-9 of 9 results.

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