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 1-6 of 6 results.

A016787 a(n) = (3*n + 1)^11.

Original entry on oeis.org

1, 4194304, 1977326743, 100000000000, 1792160394037, 17592186044416, 116490258898219, 584318301411328, 2384185791015625, 8293509467471872, 25408476896404831, 70188843638032384, 177917621779460413, 419430400000000000, 929293739471222707, 1951354384207722496
Offset: 0

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Programs

  • Magma
    [(3*n+1)^11: n in [0..20]]; // Vincenzo Librandi, Sep 29 2011
  • Mathematica
    Table[(3*n + 1)^11, {n, 0, 30}] (* Amiram Eldar, Mar 30 2022 *)

Formula

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016777(n)^11.
Sum_{n>=0} 1/a(n) = 7388*Pi^11/(2511058725*sqrt(3)) + 88573*zeta(11)/177147. (End)
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12). - Wesley Ivan Hurt, Apr 12 2023

A016786 a(n) = (3*n+1)^10.

Original entry on oeis.org

1, 1048576, 282475249, 10000000000, 137858491849, 1099511627776, 6131066257801, 26559922791424, 95367431640625, 296196766695424, 819628286980801, 2064377754059776, 4808584372417849, 10485760000000000, 21611482313284249, 42420747482776576, 79792266297612001
Offset: 0

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Programs

  • Magma
    [(3*n+1)^10: n in [0..20]]; // Vincenzo Librandi, Sep 29 2011
  • Mathematica
    Table[(3n+1)^10,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)
    LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,1048576,282475249,10000000000,137858491849,1099511627776,6131066257801,26559922791424,95367431640625,296196766695424,819628286980801},20] (* Harvey P. Dale, May 14 2019 *)

Formula

a(n) = A008454(A016777(n)). - Michel Marcus, Jun 15 2016
Sum_{n>=0} 1/a(n) = PolyGamma(9, 1/3)/21427701120. - Amiram Eldar, Mar 29 2022

A016941 a(n) = (6*n + 2)^9.

Original entry on oeis.org

512, 134217728, 20661046784, 512000000000, 5429503678976, 35184372088832, 165216101262848, 618121839509504, 1953125000000000, 5416169448144896, 13537086546263552, 31087100296429568, 66540410775079424, 134217728000000000, 257327417311663616, 472161363286556672
Offset: 0

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Programs

  • Magma
    [(6*n+2)^9: n in [0..25]]; // Vincenzo Librandi, May 05 2011
  • Mathematica
    (6*Range[0,20]+2)^9 (* or *) LinearRecurrence[ {10,-45,120,-210,252,-210,120,-45,10,-1},{512,134217728,20661046784,512000000000,5429503678976,35184372088832,165216101262848,618121839509504,1953125000000000,5416169448144896},20] (* Harvey P. Dale, Sep 21 2013 *)

Formula

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10). - Harvey P. Dale, Sep 21 2013
From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^9 = A016935(n)^3.
a(n) = 2^9*A016785(n).
Sum_{n>=0} 1/a(n) = 809*Pi^9/(14285134080*sqrt(3)) + 9841*zeta(9)/10077696. (End)

A016788 a(n) = (3*n+1)^12.

Original entry on oeis.org

1, 16777216, 13841287201, 1000000000000, 23298085122481, 281474976710656, 2213314919066161, 12855002631049216, 59604644775390625, 232218265089212416, 787662783788549761, 2386420683693101056, 6582952005840035281, 16777216000000000000, 39959630797262576401
Offset: 0

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Formula

a(n) = A008456(A016777(n)). - Michel Marcus, Jun 16 2016
Sum_{n>=0} 1/a(n) = PolyGamma(11, 1/3)/21213424108800. - Amiram Eldar, Mar 30 2022

A017205 a(n) = (9*n + 3)^9.

Original entry on oeis.org

19683, 5159780352, 794280046581, 19683000000000, 208728361158759, 1352605460594688, 6351461955384057, 23762680013799936, 75084686279296875, 208215748530929664, 520411082988487293, 1195092568622310912, 2558036924386500591, 5159780352000000000, 9892530380752880769
Offset: 0

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Formula

From Amiram Eldar, Oct 03 2024: (Start)
a(n) = A017197(n)^9 = 3^9 * A016785(n).
Sum_{n>=0} 1/a(n) = 1618*Pi^9/(1098337086315*sqrt(3)) + 9841*zeta(9)/387420489. (End)

A017577 a(n) = (12n+4)^9.

Original entry on oeis.org

262144, 68719476736, 10578455953408, 262144000000000, 2779905883635712, 18014398509481984, 84590643846578176, 316478381828866048, 1000000000000000000, 2773078757450186752, 6930988311686938624, 15916595351771938816, 34068690316840665088, 68719476736000000000
Offset: 0

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Programs

  • Mathematica
    (12*Range[0,30]+4)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{262144,68719476736,10578455953408,262144000000000,2779905883635712,18014398509481984,84590643846578176,316478381828866048,1000000000000000000,2773078757450186752},40] (* Harvey P. Dale, Sep 07 2018 *)

Formula

From Amiram Eldar, Jul 14 2024: (Start)
a(n) = A001017(A017569(n)) = A017569(n)^9.
a(n) = 262144 * A016785(n).
Sum_{n>=0} 1/a(n) = 809*Pi^9/(7313988648960*sqrt(3)) + 9841*zeta(9)/5159780352. (End)

Extensions

More terms from Amiram Eldar, Jul 14 2024
Showing 1-6 of 6 results.