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 1-5 of 5 results.

A016785 a(n) = (3*n + 1)^9.

Original entry on oeis.org

1, 262144, 40353607, 1000000000, 10604499373, 68719476736, 322687697779, 1207269217792, 3814697265625, 10578455953408, 26439622160671, 60716992766464, 129961739795077, 262144000000000, 502592611936843, 922190162669056, 1628413597910449, 2779905883635712
Offset: 0

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Programs

  • Magma
    [(3*n+1)^9 : n in [0..20]]; // Vincenzo Librandi, Sep 28 2011
  • Maple
    A016785:=n->(3*n+1)^9; seq(A016785(k), k=0..100); # Wesley Ivan Hurt, Nov 05 2013
  • Mathematica
    Table[(3*n+1)^9, {n,0,100}] (* Wesley Ivan Hurt, Nov 05 2013 *)
    LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,262144,40353607,1000000000,10604499373,68719476736,322687697779,1207269217792,3814697265625,10578455953408},100] (* Harvey P. Dale, Aug 17 2014 *)

Formula

From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016777(n)^9 = A016779(n)^3.
Sum_{n>=0} 1/a(n) = 1618*Pi^9/(55801305*sqrt(3)) + 9841*zeta(9)/3^9. (End)

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

A016940 a(n) = (6*n + 2)^8.

Original entry on oeis.org

256, 16777216, 1475789056, 25600000000, 208827064576, 1099511627776, 4347792138496, 14048223625216, 39062500000000, 96717311574016, 218340105584896, 457163239653376, 899194740203776, 1677721600000000, 2992179271065856, 5132188731375616, 8507630225817856
Offset: 0

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Programs

  • Magma
    [(6*n+2)^8: n in [0..20]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    (6*Range[0,20]+2)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{256,16777216,1475789056,25600000000,208827064576,1099511627776,4347792138496,14048223625216,39062500000000},20] (* Harvey P. Dale, Sep 06 2020 *)

Formula

From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^8 = A016934(n)^4 = A016936(n)^2.
a(n) = 2^8*A016784(n).
Sum_{n>=0} 1/a(n) = PolyGamma(7, 1/3)/8465264640. (End)

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

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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Author

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Crossrefs

Programs

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
Showing 1-5 of 5 results.