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.

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A197983 Round((10*n+1/n)^n).

Original entry on oeis.org

11, 420, 27910, 2624603, 318800200, 47439020042, 8353801755006, 1698808167100876, 391746480089540115, 101004512021025221012, 28791615763253886202480, 8990685731188213404550239, 3052132045866636492112058599
Offset: 1

Views

Author

Vincenzo Librandi, Oct 20 2011

Keywords

Crossrefs

Programs

  • Magma
    [Round((10*n+1/n)^n): n in [1..20]]
  • Mathematica
    Table[Floor[1/2+(10n+1/n)^n],{n,20}] (* Harvey P. Dale, May 02 2012 *)

A197984 Round((11*n+1/n)^n).

Original entry on oeis.org

12, 506, 37037, 3834009, 512501792, 83914215402, 16258109291002, 3637416562713075, 922786228220640101, 261741863272493596614, 82078032321730681299097, 28195269239973685901676782, 10529425953839699619063326836
Offset: 1

Views

Author

Vincenzo Librandi, Oct 20 2011

Keywords

Crossrefs

Programs

  • Magma
    [Round((11*n+1/n)^n): n in [1..20]]
  • Mathematica
    Table[Round[(11n+1/n)^n],{n,20}] (* Harvey P. Dale, May 07 2021 *)

A197986 a(n) = round((n+1/n)^3).

Original entry on oeis.org

8, 16, 37, 77, 141, 235, 364, 536, 756, 1030, 1364, 1764, 2236, 2786, 3420, 4144, 4964, 5886, 6916, 8060, 9324, 10714, 12236, 13896, 15700, 17654, 19764, 22036, 24476, 27090, 29884, 32864, 36036, 39406, 42980, 46764, 50764
Offset: 1

Views

Author

Vincenzo Librandi, Oct 21 2011

Keywords

Crossrefs

Programs

  • Magma
    [Round((n+1/n)^3): n in [1..60]]
    
  • Mathematica
    Table[Round[(n+1/n)^3],{n,40}] (* or *) Join[{8,16,37,77,141,235}, LinearRecurrence[ {4,-6,4,-1},{364,536,756,1030},40]] (* Harvey P. Dale, Apr 05 2012 *)
  • SageMath
    [8,16,37,77,141,235]+[n*(n^2+3) for n in range(7,51)] # G. C. Greubel, Feb 04 2024

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), with a(1)= 8, a{2}=16, a(3)=37, a(4)=77, a(5)=141, a(6)=235, a(7)=364, a(8)=536, a(9)=756, a(10)=1030. - Harvey P. Dale, Apr 05 2012
From G. C. Greubel, Feb 04 2024: (Start)
a(n) = n*(n^2+3) for n > 6, with a(1)=8, a(2)=16, a(3)=37, a(4)=77, a(5)=141, a(6)=235.
G.f.: x*(8 - 16*x + 21*x^2 - 7*x^3 - x^4 + x^5 - x^6 + 3*x^7 - 3*x^8 + x^9)/(1-x)^4.
E.g.f.: 4*x + x^2 + x^3/3! + x^4/4! + x^5/5! + x^6/6! + x*(4 + 3*x + x^2)*exp(x). (End)

A198070 a(n) = round((n+1/n)^5).

Original entry on oeis.org

32, 98, 412, 1387, 3802, 8918, 18593, 35409, 62785, 105101, 167817, 257593, 382409, 551685, 776401, 1069217, 1444593, 1918909, 2510585, 3240201, 4130616, 5207092, 6497408, 8031984, 9844000, 11969516, 14447592, 17320408
Offset: 1

Views

Author

Vincenzo Librandi, Oct 21 2011

Keywords

Crossrefs

Programs

Formula

a(n) = n*(n^4+5*n^2+10) = A197904(n)-1 for n>20. - Bruno Berselli, Oct 27 2011

A198071 Round((n+1/n)^6).

Original entry on oeis.org

64, 244, 1372, 5893, 19771, 54992, 132810, 287700, 572042, 1061520, 1861242, 3112580, 5000730, 7762992, 11697770, 17174292, 24643050, 34646960, 47833242, 64966020, 86939642, 114792720, 149722890, 193102292, 246493770
Offset: 1

Views

Author

Vincenzo Librandi, Oct 21 2011

Keywords

Crossrefs

Programs

  • Magma
    [Round((n+1/n)^6): n in [1..60]];
  • Mathematica
    Table[Round[(n+1/n)^6],{n,30}] (* Harvey P. Dale, Nov 11 2013 *)

A198072 Round((n+1/n)^7).

Original entry on oeis.org

128, 610, 4572, 25045, 102807, 339120, 948645, 2337564, 5211940, 10721354, 20642867, 37610343, 65394163, 109236389, 176246402, 275862066, 420381442, 625570112, 911349138, 1302568702, 1829872466, 2530657692
Offset: 1

Views

Author

Vincenzo Librandi, Oct 21 2011

Keywords

Crossrefs

Programs

  • Magma
    [Round((n+1/n)^7): n in [1..60]];
  • Mathematica
    Table[Floor[(n+1/n)^7+1/2],{n,30}] (* Harvey P. Dale, Oct 26 2011 *)

A198073 Round((n+1/n)^8).

Original entry on oeis.org

256, 1526, 15242, 106442, 534597, 2091240, 6776036, 18992711, 47486564, 108285671, 228948163, 454458310, 855154435, 1537112038, 2655445795, 4431034438, 7171212835, 11295015910, 17363599363, 26116502470, 38514458563
Offset: 1

Views

Author

Vincenzo Librandi, Oct 21 2011

Keywords

Crossrefs

Programs

  • Magma
    [Round((n+1/n)^8): n in [1..40]];

A198074 Round((n+1/n)^9).

Original entry on oeis.org

512, 3815, 50805, 452377, 2779906, 12895977, 48400258, 154315776, 432655358, 1093685273, 2539243268, 5491371251, 11182788770, 21629362253, 40008716648, 71173490664, 122332454247, 203937787267, 330822261551
Offset: 1

Views

Author

Vincenzo Librandi, Oct 21 2011

Keywords

Crossrefs

Programs

  • Magma
    [Round((n+1/n)^9): n in [1..40]];

A198075 Round((n+1/n)^10).

Original entry on oeis.org

1024, 9537, 169351, 1922602, 14455511, 79525194, 345716130, 1253815679, 3941971041, 11046221254, 28162516240, 66354069277, 146236468527, 304356025989, 602797997503, 1143224193789, 2086847748927, 3682210047877
Offset: 1

Views

Author

Vincenzo Librandi, Oct 21 2011

Keywords

Crossrefs

Programs

  • Magma
    [Round((n+1/n)^10): n in [1..40]];

A198076 Round((n+1/2)^n).

Original entry on oeis.org

2, 6, 43, 410, 5033, 75419, 1334839, 27249053, 630249410, 16288946268, 465239139606, 14551915228367, 494696673952512, 18161513224841276, 716102966059713316, 30181658957863752410, 1354087807629298185930, 64430442087414935111822
Offset: 1

Views

Author

Vincenzo Librandi, Oct 21 2011

Keywords

Crossrefs

Cf. A014056.

Programs

  • Magma
    [Round((n+1/2)^n): n in [1..20]];
  • Mathematica
    Table[Round[(n+1/2)^n],{n,30}] (* Harvey P. Dale, Aug 10 2019 *)
Previous Showing 11-20 of 23 results. Next