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.

A016924 a(n) = (6*n + 1)^4.

Original entry on oeis.org

1, 2401, 28561, 130321, 390625, 923521, 1874161, 3418801, 5764801, 9150625, 13845841, 20151121, 28398241, 38950081, 52200625, 68574961, 88529281, 112550881, 141158161, 174900625, 214358881, 260144641, 312900721, 373301041, 442050625, 519885601, 607573201, 705911761
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

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

Programs

Formula

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^4 = A016922(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(3, 1/6)/7776. (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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