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.

A016752 a(n) = (2*n)^12.

Original entry on oeis.org

0, 4096, 16777216, 2176782336, 68719476736, 1000000000000, 8916100448256, 56693912375296, 281474976710656, 1156831381426176, 4096000000000000, 12855002631049216, 36520347436056576, 95428956661682176, 232218265089212416, 531441000000000000, 1152921504606846976
Offset: 0

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Author

Keywords

Crossrefs

Cf. A016764.

Programs

  • Magma
    [(2*n)^12: n in [0..20]]; // Vincenzo Librandi, Sep 05 2011
    
  • Maple
    A016752:=n->(2*n)^12: seq(A016752(n), n=0..30); # Wesley Ivan Hurt, Sep 15 2018
  • Mathematica
    (2*Range[0,20])^12 (* or *) LinearRecurrence[{13,-78,286,-715,1287,-1716, 1716,-1287, 715, -286,78,-13,1},{0,4096,16777216,2176782336, 68719476736, 1000000000000, 8916100448256,56693912375296, 281474976710656, 1156831381426176, 4096000000000000, 12855002631049216, 36520347436056576}, 20] (* Harvey P. Dale, Apr 05 2018 *)
  • PARI
    vector(30, n, n--; (2*n)^12) \\ G. C. Greubel, Sep 15 2018

Formula

From Amiram Eldar, Oct 11 2020: (Start)
Sum_{n>=1} 1/a(n) = 691*Pi^12/2615348736000.
Sum_{n>=1} (-1)^(n+1)/a(n) = 1414477*Pi^12/5356234211328000. (End)

A016836 a(n) = (4n+2)^12.

Original entry on oeis.org

4096, 2176782336, 1000000000000, 56693912375296, 1156831381426176, 12855002631049216, 95428956661682176, 531441000000000000, 2386420683693101056, 9065737908494995456, 30129469486639681536, 89762301673555234816, 244140625000000000000, 614787626176508399616
Offset: 0

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Programs

  • Mathematica
    Table[(4*n+2)^12, {n, 0, 20}] (* Amiram Eldar, Apr 21 2023 *)

Formula

From Amiram Eldar, Apr 21 2023: (Start)
a(n) = A016825(n)^12.
a(n) = 2^12*A016764(n).
Sum_{n>=0} 1/a(n) = 691*Pi^12/2615987404800. (End)

A016956 a(n) = (6*n + 3)^12.

Original entry on oeis.org

531441, 282429536481, 129746337890625, 7355827511386641, 150094635296999121, 1667889514952984961, 12381557655576425121, 68952523554931640625, 309629344375621415601, 1176246293903439668001, 3909188328478827879681, 11646329922777311412561, 31676352024078369140625
Offset: 0

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Programs

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016945(n)^12 = A016946(n)^6 = A016947(n)^4 = A016948(n)^3 = A016950(n)^2..
a(n) = 3^12*A016764(n).
Sum_{n>=0} 1/a(n) = 691*Pi^12/339414785740800. (End)

A017124 a(n) = (8*n + 4)^12.

Original entry on oeis.org

16777216, 8916100448256, 4096000000000000, 232218265089212416, 4738381338321616896, 52654090776777588736, 390877006486250192896, 2176782336000000000000, 9774779120406941925376, 37133262473195501387776, 123410307017276135571456, 367666387654882241806336
Offset: 0

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Programs

Formula

From Amiram Eldar, Apr 25 2023: (Start)
a(n) = A017113(n)^12.
a(n) = 2^12*A016836(n) = 2^24*A016764(n).
Sum_{n>=0} 1/a(n) = 691*Pi^12/10715084410060800. (End)

A017340 a(n) = (10*n + 5)^12.

Original entry on oeis.org

244140625, 129746337890625, 59604644775390625, 3379220508056640625, 68952523554931640625, 766217865410400390625, 5688009063105712890625, 31676352024078369140625, 142241757136172119140625, 540360087662636962890625, 1795856326022129150390625, 5350250105473711181640625
Offset: 0

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Programs

Formula

G.f.: -244140625*(x^12 + 531428*x^11 + 237231970*x^10 + 10708911188*x^9 + 121383780207*x^8 + 477020564424*x^7 + 743288515164*x^6 + 477020564424*x^5 + 121383780207*x^4 + 10708911188*x^3 + 237231970*x^2 + 531428*x + 1)/(x-1)^13. - Colin Barker, Nov 14 2012
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^12.
a(n) = 5^12 * A016764(n).
Sum_{n>=0} 1/a(n) = 691*Pi^12/155925000000000000. (End)
Showing 1-5 of 5 results.