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 1-8 of 8 results.

A128074 a(n) = (n^3+n)*9^n.

Original entry on oeis.org

0, 18, 810, 21870, 446148, 7676370, 117979902, 1674039150, 22384294920, 285916320882, 3521652245010, 42113381995278, 491427393476940, 5617523480607090, 63094193590782438, 697970937800860110
Offset: 0

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Links

Crossrefs

Cf. A128796; A128960; A128985; A129002.

Programs

  • Magma
    [(n^3 + n) * 9^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2012
  • Mathematica
    Table[(n^3+n)9^n,{n,20}] (* or *) LinearRecurrence[{36,-486,2916,-6561}, {18,810,21870,446148},20] (* Harvey P. Dale, Jun 16 2011 *)
  • PARI
    A128074(n)=(n^3+n)*9^n \\ M. F. Hasler, Oct 06 2014

Formula

a(1)=18, a(2)=810, a(3)=21870, a(4)=446148, a(n)=36*a(n-1)- 486*a(n-2)+ 2916*a(n-3)-6561*a(n-4). - Harvey P. Dale, Jun 16 2011
G.f.: 18*x*(1+9*x+81*x^2)/(1-9*x)^4. - Harvey P. Dale, Jun 16 2011

Extensions

Extended to a(0)=0 by M. F. Hasler, Oct 06 2014

A119635 a(n) = n*(1 + n^2)*2^n.

Original entry on oeis.org

4, 40, 240, 1088, 4160, 14208, 44800, 133120, 377856, 1034240, 2748416, 7127040, 18104320, 45187072, 111083520, 269484032, 646184960, 1533542400, 3606052864, 8409579520, 19465764864, 44753223680, 102257131520, 232330887168
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Links

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Programs

  • GAP
    List([1..30],n->n*(n^2+1)*2^n); # Muniru A Asiru, Mar 04 2019
  • Magma
    [(n^3 + n)*2^n: n in [1..30]]; // Vincenzo Librandi, Feb 22 2013
  • Maple
    [(n^3+n)*2^n$n=1..30]; # Muniru A Asiru, Mar 04 2019
  • Mathematica
    Table[(n^3 + n)*2^n, {n, 30}] (* or *) CoefficientList[Series[4(1 +2x + 4x^2)/(1-2x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)
  • PARI
    {a(n) = n*(1+n^2)*2^n}; \\ G. C. Greubel, Mar 04 2019
  • Sage
    [n*(1+n^2)*2^n for n in (1..30)] # G. C. Greubel, Mar 04 2019

Formula

G.f.: 4*x*(1 + 2*x + 4*x^2)/(1 - 2*x)^4. - Vincenzo Librandi, Feb 22 2013
E.g.f.: 4*x*(1 + 3*x + 2*x^2)*exp(2*x). - G. C. Greubel, Mar 04 2019

A121607 (n^3+n)*3^n.

Original entry on oeis.org

6, 90, 810, 5508, 31590, 161838, 765450, 3411720, 14526054, 59639490, 237731274, 924707340, 3523453830, 13191428502, 48642794730, 177008116752, 636661003590, 2266409860650, 7994034370026, 27964010896020, 97092998430246
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Links

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Programs

  • Magma
    [(n^3 + n)*3^n: n in [1..30]]; // Vincenzo Librandi, Feb 22 2013
  • Mathematica
    Table[(n^3 + n)*3^n, {n, 30}] (* or *) CoefficientList[Series[6 (1 + 3 x + 9 x^2)/(1 - 3 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

Formula

G.f.: 6*x*(1 + 3*x + 9*x^2)/(1 - 3*x)^4. - Vincenzo Librandi, Feb 22 2013

A127369 (n^3+n)*4^n.

Original entry on oeis.org

8, 160, 1920, 17408, 133120, 909312, 5734400, 34078720, 193462272, 1059061760, 5628755968, 29192355840, 148310589440, 740344987648, 3639984783360, 17660905521152, 84696755077120, 402008938905600, 1890610243960832
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Links

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Programs

  • Magma
    [(n^3 + n) * 4^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
  • Mathematica
    Table[(n^3 + n) 4^n, {n, 20}] (* Vincenzo Librandi Feb 22 2013 *)
LinearRecurrence[{16,-96,256,-256},{8,160,1920,17408},20] (* Harvey P. Dale, Aug 14 2021 *)

Formula

G.f.: 8*x*(1+4*x+16*x^2)/(1-4*x)^4. [R. J. Mathar, Dec 19 2008]

A128013 a(n) = (n^3 +n)*5^n.

Original entry on oeis.org

10, 250, 3750, 42500, 406250, 3468750, 27343750, 203125000, 1441406250, 9863281250, 65527343750, 424804687500, 2697753906250, 16833496093750, 103454589843750, 627441406250000, 3761291503906250, 22315979003906250
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Links

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Programs

  • Magma
    [(n^3 + n)*5^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
  • Magma
    I:=[10,250,3750,42500]; [n le 4 select I[n] else 20*Self(n-1)-150*Self(n-2)+500*Self(n-3)-625*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 23 2013
  • Mathematica
    Table[(n^3 + n) 5^n, {n, 30}] (* or *) CoefficientList[Series[10 (1 + 5 x + 25 x^2)/(1 - 5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)
  • PARI
    for(n=1, 30, print1((n^3 +n)*5^n, ", ")) \\ G. C. Greubel, May 08 2018

Formula

G.f.: 10*x(1+5*x+25*x^2)/(1-5*x)^4. - Vincenzo Librandi, Feb 22 2013
a(n) = 20*a(n-1) -150*a(n-2) +500*a(n-3) -625*a(n-4). - Vincenzo Librandi, Feb 23 2013

A128043 (n^3+n)*6^n.

Original entry on oeis.org

12, 360, 6480, 88128, 1010880, 10357632, 97977600, 873400320, 7437339648, 61070837760, 486873649152, 3787601264640, 28864133775360, 216128364576768, 1593927097712640, 11600403939459072, 83448431062548480
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Links

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Programs

  • Magma
    [(n^3 + n)*6^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
  • Mathematica
    Table[(n^3 + n) * 6^n, {n, 30}] (* or *) CoefficientList[Series[12 (1 + 6 x + 36 x^2)/(1 - 6 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

Formula

G.f.: 12*x*(1 + 6*x + 36*x^2)/(1 - 6*x)^4. - Vincenzo Librandi, Feb 22 2013

A128048 (n^3+n)*8^n.

Original entry on oeis.org

16, 640, 15360, 278528, 4259840, 58195968, 734003200, 8724152320, 99052683264, 1084479242240, 11527692222464, 119571889520640, 1214960348692480, 12129812277624832, 119275021381140480, 1157425104234217472
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Links

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Programs

  • Magma
    [(n^3 + n)*8^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
  • Magma
    I:=[16,640,15360,278528]; [n le 4 select I[n] else 32*Self(n-1)-384*Self(n-2)+2048*Self(n-3)-4096*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 23 2013
  • Mathematica
    Table[(n^3 + n) 8^n, {n, 30}] (* or *) CoefficientList[Series[16 (1 + 8 x + 64 x^2)/(1 - 8 x)^4, {x, 0, 20}],x] (* Vincenzo Librandi, Feb 22 2013 *)

Formula

G.f.: 16*x*(1+8*x+64*x^2)/(1-8*x)^4. - Vincenzo Librandi, Feb 22 2013
a(n) = 32*a(n-1) -384*a(n-2) +2048*a(n-3) -4096*a(n-4). - Vincenzo Librandi, Feb 23 2013

A128051 (n^3+n)*7^n.

Original entry on oeis.org

14, 490, 10290, 163268, 2184910, 26118078, 288240050, 2997696520, 29780961966, 285300001490, 2653572489106, 24083839729740, 214124712999470, 1870539234917542, 16094233518706770, 136653810502199312
Offset: 1

Views

Author

Mohammad K. Azarian, May 02 2007

Keywords

Links

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Programs

  • Magma
    [(n^3 + n)*7^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
  • Mathematica
    Table[(n^3 + n) * 7^n, {n, 30}] (* or *) CoefficientList[Series[14 (1 + 7 x + 49 x^2)/(1 - 7 x)^4, {x, 0, 20}], x] (* Vincenzo Librandi, Feb 22 2013 *)

Formula

G.f.: 14*x*(1 + 7*x + 49*x^2)/(1 - 7*x)^4. - Vincenzo Librandi, Feb 22 2013
Showing 1-8 of 8 results.

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

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