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.

A016954 a(n) = (6n+3)^10.

Original entry on oeis.org

59049, 3486784401, 576650390625, 16679880978201, 205891132094649, 1531578985264449, 8140406085191601, 34050628916015625, 119042423827613001, 362033331456891249, 984930291881790849, 2446194060654759801, 5631351470947265625, 12157665459056928801
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A008454, A016762, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952, A016953.
Subsequence of A008454.

Programs

Formula

From Wesley Ivan Hurt, Aug 22 2016: (Start)
G.f.: 59049*(1 + 59038*x + 9116141*x^2 + 178300904*x^3 + 906923282*x^4 + 1527092468*x^5 + 906923282*x^6 + 178300904*x^7 + 9116141*x^8 + 59038*x^9 + x^10)/(1-x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>10.
a(n) = A008454(A016945(n)). (End)
From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016946(n)^5 = A016949(n)^2.
a(n) = 3^10*A016762(n).
Sum_{n>=0} 1/a(n) = 31*Pi^10/171421608960. (End)

A016750 a(n) = (2*n)^10.

Original entry on oeis.org

0, 1024, 1048576, 60466176, 1073741824, 10000000000, 61917364224, 289254654976, 1099511627776, 3570467226624, 10240000000000, 26559922791424, 63403380965376, 141167095653376, 296196766695424, 590490000000000, 1125899906842624, 2064377754059776, 3656158440062976
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016762.

Programs

  • Magma
    [(2*n)^10: n in [0..20]]; // Vincenzo Librandi, Sep 05 2011
  • Maple
    A016750:=n->(2*n)^10: seq(A016750(n), n=0..30); # Wesley Ivan Hurt, Sep 15 2018
  • Mathematica
    Table[(2*n)^10, {n,0,30}] (* G. C. Greubel, Sep 15 2018 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{0,1024,1048576,60466176,1073741824,10000000000,61917364224,289254654976,1099511627776,3570467226624,10240000000000},30]   (* Harvey P. Dale, May 11 2022 *)
  • PARI
    vector(30, n, n--; (2*n)^10) \\ G. C. Greubel, Sep 15 2018

Formula

G.f.: -1024*x*(1+x)*(x^8 + 1012*x^7 + 46828*x^6 + 408364*x^5 + 901990*x^4 + 408364*x^3 + 46828*x^2 + 1012*x + 1)/(x-1)^11. - R. J. Mathar, Jul 07 2017
From Amiram Eldar, Oct 11 2020: (Start)
Sum_{n>=1} 1/a(n) = Pi^10/95800320.
Sum_{n>=1} (-1)^(n+1)/a(n) = 73*Pi^10/7007109120. (End)

A016834 a(n) = (4n+2)^10.

Original entry on oeis.org

1024, 60466176, 10000000000, 289254654976, 3570467226624, 26559922791424, 141167095653376, 590490000000000, 2064377754059776, 6278211847988224, 17080198121677824, 42420747482776576, 97656250000000000, 210832519264920576, 430804206899405824, 839299365868340224
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016762, A016825.

Programs

  • Mathematica
    Table[(4*n+2)^10, {n, 0, 20}] (* Amiram Eldar, Apr 21 2023 *)

Formula

From Amiram Eldar, Apr 21 2023: (Start)
a(n) = A016825(n)^10.
a(n) = 2^10*A016762(n).
Sum_{n>=0} 1/a(n) = 31*Pi^10/2972712960. (End)

A017338 a(n) = (10*n + 5)^10.

Original entry on oeis.org

9765625, 576650390625, 95367431640625, 2758547353515625, 34050628916015625, 253295162119140625, 1346274334462890625, 5631351470947265625, 19687440434072265625, 59873693923837890625, 162889462677744140625, 404555773570791015625, 931322574615478515625
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016762, A017329.

Programs

  • Magma
    [(10*n+5)^10: n in [0..10]]; // Vincenzo Librandi, Aug 02 2011
  • Mathematica
    (10 Range[0,20]+5)^10 (* or *) LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{9765625,576650390625,95367431640625,2758547353515625,34050628916015625,253295162119140625,1346274334462890625,5631351470947265625,19687440434072265625,59873693923837890625,162889462677744140625},20] (* Harvey P. Dale, Jul 18 2021 *)

Formula

G.f.: -9765625*(x^10 + 59038*x^9 + 9116141*x^8 + 178300904*x^7 + 906923282*x^6 + 1527092468*x^5 + 906923282*x^4 + 178300904*x^3 + 9116141*x^2 + 59038*x + 1)/(x-1)^11. - Colin Barker, Nov 14 2012
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^10.
a(n) = 5^10 * A016762(n).
Sum_{n>=0} 1/a(n) = 31*Pi^10/28350000000000. (End)

A017122 a(n) = (8*n + 4)^10.

Original entry on oeis.org

1048576, 61917364224, 10240000000000, 296196766695424, 3656158440062976, 27197360938418176, 144555105949057024, 604661760000000000, 2113922820157210624, 6428888932339941376, 17490122876598091776, 43438845422363213824, 100000000000000000000, 215892499727278669824
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016762, A016834, A017113.

Programs

  • Magma
    [(8*n+4)^10: n in [0..15] ]; // Vincenzo Librandi, Jul 21 2011
  • Mathematica
    Table[(8*n + 4)^10, {n, 0, 20}] (* Amiram Eldar, Apr 25 2023 *)

Formula

G.f.: ( -1048576 - 61905829888*x - 9558966665216*x^2 - 186962048712704*x^3 - 950977987346432*x^4 - 1601272511725568*x^5 - 950977987346432*x^6 - 186962048712704*x^7 - 9558966665216*x^8 - 61905829888*x^9 - 1048576*x^10 ) / ( (x-1)^11 ). - R. J. Mathar, May 08 2015
From Amiram Eldar, Apr 25 2023: (Start)
a(n) = A017113(n)^10.
a(n) = 2^10*A016834(n) = 2^20*A016762(n).
Sum_{n>=0} 1/a(n) = 31*Pi^10/3044058071040. (End)
Showing 1-5 of 5 results.

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

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