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.

A016925 a(n) = (6*n + 1)^5.

Original entry on oeis.org

1, 16807, 371293, 2476099, 9765625, 28629151, 69343957, 147008443, 282475249, 503284375, 844596301, 1350125107, 2073071593, 3077056399, 4437053125, 6240321451, 8587340257, 11592740743, 15386239549, 20113571875, 25937424601, 33038369407, 41615795893, 51888844699
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016926.

Programs

Formula

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^5.
Sum_{n>=0} 1/a(n) = ((1-1/2^5)*(1-1/3^5)*zeta(5) + 11*(Pi/3)^5/(8*sqrt(3)))/2 (Štofka, 2013). (End)

A016926 a(n) = (6*n + 1)^6.

Original entry on oeis.org

1, 117649, 4826809, 47045881, 244140625, 887503681, 2565726409, 6321363049, 13841287201, 27680640625, 51520374361, 90458382169, 151334226289, 243087455521, 377149515625, 567869252041, 832972004929, 1194052296529, 1677100110841, 2313060765625, 3138428376721
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016925.

Programs

  • Magma
    [(6*n+1)^6: n in [0..40]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    (6*Range[0,20]+1)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,117649,4826809,47045881,244140625,887503681,2565726409},20] (* Harvey P. Dale, Aug 19 2019 *)

Formula

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^6 = A016922(n)^3 = A016923(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(5, 1/6)/5598720. (End)

A016927 a(n) = (6*n + 1)^7.

Original entry on oeis.org

1, 823543, 62748517, 893871739, 6103515625, 27512614111, 94931877133, 271818611107, 678223072849, 1522435234375, 3142742836021, 6060711605323, 11047398519097, 19203908986159, 32057708828125, 51676101935731, 80798284478113, 122987386542487, 182803912081669
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016925, A016926.

Programs

  • Magma
    [(6*n+1)^7: n in [0..40]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    (6*Range[0,20]+1)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,823543,62748517,893871739,6103515625,27512614111,94931877133,271818611107},20] (* Harvey P. Dale, May 12 2015 *)

Formula

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Harvey P. Dale, May 12 2015
From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^7.
Sum_{n>=0} 1/a(n) = 301*Pi^7/(1049760*sqrt(3)) + 138811*zeta(7)/279936. (End)

A016928 a(n) = (6*n + 1)^8.

Original entry on oeis.org

1, 5764801, 815730721, 16983563041, 152587890625, 852891037441, 3512479453921, 11688200277601, 33232930569601, 83733937890625, 191707312997281, 406067677556641, 806460091894081, 1517108809906561, 2724905250390625, 4702525276151521, 7837433594376961
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927.

Programs

Formula

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^8 = A016922(n)^4 = A016924(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(7, 1/6)/8465264640. (End)

A016929 a(n) = (6*n + 1)^9.

Original entry on oeis.org

1, 40353607, 10604499373, 322687697779, 3814697265625, 26439622160671, 129961739795077, 502592611936843, 1628413597910449, 4605366583984375, 11694146092834141, 27206534396294947, 58871586708267913, 119851595982618319, 231616946283203125, 427929800129788411
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927, A016928.

Programs

  • Magma
    [(6*n+1)^9: n in [0..25]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    (6*Range[0,20]+1)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,40353607,10604499373,322687697779,3814697265625,26439622160671,129961739795077,502592611936843,1628413597910449,4605366583984375},20] (* Harvey P. Dale, Mar 22 2015 *)

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, Mar 22 2015
From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^9 = A016923(n)^3.
Sum_{n>=0} 1/a(n) = 15371*Pi^9/(529079040*sqrt(3)) + 5028751*zeta(9)/10077696. (End)

A016930 a(n) = (6*n + 1)^10.

Original entry on oeis.org

1, 282475249, 137858491849, 6131066257801, 95367431640625, 819628286980801, 4808584372417849, 21611482313284249, 79792266297612001, 253295162119140625, 713342911662882601, 1822837804551761449, 4297625829703557649, 9468276082626847201, 19687440434072265625
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927, A016928, A016929.

Programs

  • Magma
    [(6*n+1)^10: n in [0..25]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    (6 Range[0, 15] + 1)^10 (* Wesley Ivan Hurt, Jan 15 2022 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,282475249,137858491849,6131066257801,95367431640625,819628286980801,4808584372417849,21611482313284249,79792266297612001,253295162119140625,713342911662882601},20] (* Harvey P. Dale, Sep 05 2023 *)

Formula

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^10 = A016922(n)^5 = A016925(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(9, 1/6)/21941965946880. (End)

A016931 a(n) = (6*n + 1)^11.

Original entry on oeis.org

1, 1977326743, 1792160394037, 116490258898219, 2384185791015625, 25408476896404831, 177917621779460413, 929293739471222707, 3909821048582988049, 13931233916552734375, 43513917611435838661, 122130132904968017083, 313726685568359708377, 747993810527520928879
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927, A016928, A016929, A016930.

Programs

Formula

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^11.
Sum_{n>=0} 1/a(n) = 1261501*Pi^11/(428554022400*sqrt(3)) + 181308931*zeta(11)/362797056. (End)

A016932 a(n) = (6*n + 1)^12.

Original entry on oeis.org

1, 13841287201, 23298085122481, 2213314919066161, 59604644775390625, 787662783788549761, 6582952005840035281, 39959630797262576401, 191581231380566414401, 766217865410400390625, 2654348974297586158321, 8182718904632857144561, 22902048046490258711521
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927, A016928, A016929, A016930, A016931.

Programs

  • Magma
    [(6*n+1)^12: n in [0..20]]; // Vincenzo Librandi, May 04 2011
  • Mathematica
    Table[(6*n + 1)^12, {n, 0, 12}] (* Amiram Eldar, Mar 28 2022 *)

Formula

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^12 = A016922(n)^6 = A016923(n)^4 = A016924(n)^3 = A016926(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(11, 1/6)/86890185149644800. (End)
Showing 1-8 of 8 results.

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

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