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.

A016961 a(n) = (6*n + 4)^5.

Original entry on oeis.org

1024, 100000, 1048576, 5153632, 17210368, 45435424, 102400000, 205962976, 380204032, 656356768, 1073741824, 1680700000, 2535525376, 3707398432, 5277319168, 7339040224, 10000000000, 13382255776, 17623416832, 22877577568, 29316250624, 37129300000, 46525874176
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016793, A016957, A016958, A016959, A016960.
Subsequence of A000584.

Programs

  • Magma
    [(6*n+4)^5: n in [0..30]]; // Vincenzo Librandi, May 06 2011
  • Mathematica
    a[n_] := (6*n + 4)^5; Array[a, 20, 0] (* Amiram Eldar, Mar 31 2022 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{1024,100000,1048576,5153632,17210368,45435424},30] (* Harvey P. Dale, Jan 01 2025 *)

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016957(n)^5.
a(n) = 32*A016793(n).
Sum_{n>=0} 1/a(n) = 121*zeta(5)/7776 - Pi^5/(11664*sqrt(3)). (End)

A016962 a(n) = (6*n + 4)^6.

Original entry on oeis.org

4096, 1000000, 16777216, 113379904, 481890304, 1544804416, 4096000000, 9474296896, 19770609664, 38068692544, 68719476736, 117649000000, 192699928576, 304006671424, 464404086784, 689869781056, 1000000000000, 1418519112256, 1973822685184, 2699554153024, 3635215077376
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016794, A016957, A016958, A016959, A016960, A016961.
Subsequence of A001014.

Programs

  • Magma
    [(6*n+4)^6: n in [0..25]]; // Vincenzo Librandi, May 06 2011
  • Mathematica
    (6Range[0,20]+4)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{4096,1000000,16777216,113379904,481890304,1544804416,4096000000},20] (* Harvey P. Dale, Aug 08 2019 *)

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016957(n)^6 = A016958(n)^3 = A016959(n)^2.
a(n) = 64*A016794(n).
Sum_{n>=0} 1/a(n) = PolyGamma(5, 2/3)/5598720. (End)

A016963 a(n) = (6*n + 4)^7.

Original entry on oeis.org

16384, 10000000, 268435456, 2494357888, 13492928512, 52523350144, 163840000000, 435817657216, 1028071702528, 2207984167552, 4398046511104, 8235430000000, 14645194571776, 24928547056768, 40867559636992, 64847759419264, 100000000000000, 150363025899136, 221068140740608
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016795, A016957, A016958, A016959, A016960, A016961, A016962.
Subsequence of A001015.

Programs

  • Magma
    [(6*n+4)^7: n in [0..20]]; // Vincenzo Librandi, May 07 2011
  • Mathematica
    (6*Range[0,20]+4)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{16384,10000000,268435456,2494357888,13492928512,52523350144,163840000000,435817657216},20] (* Harvey P. Dale, Mar 03 2018 *)

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016957(n)^7.
a(n) = 2^7*A016795(n).
Sum_{n>=0} 1/a(n) = 1093*zeta(7)/279936 - 7*Pi^7/(3149280*sqrt(3)). (End)

A016964 a(n) = (6*n + 4)^8.

Original entry on oeis.org

65536, 100000000, 4294967296, 54875873536, 377801998336, 1785793904896, 6553600000000, 20047612231936, 53459728531456, 128063081718016, 281474976710656, 576480100000000, 1113034787454976, 2044140858654976, 3596345248055296, 6095689385410816, 10000000000000000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016796, A016957, A016958, A016959, A016960, A016961, A016962, A016963.
Subsequence of A001016.

Programs

  • Magma
    [(6*n+4)^8: n in [0..20]]; // Vincenzo Librandi, May 07 2011
  • Mathematica
    (6*Range[0,20]+4)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{65536,100000000,4294967296,54875873536,377801998336,1785793904896,6553600000000,20047612231936,53459728531456},20] (* Harvey P. Dale, Dec 26 2018 *)

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016957(n)^8 = A016958(n)^4 = A016960(n)^2.
a(n) = 2^8*A016796(n).
Sum_{n>=0} 1/a(n) = PolyGamma(7, 2/3)/8465264640. (End)

A016965 a(n) = (6*n + 4)^9.

Original entry on oeis.org

262144, 1000000000, 68719476736, 1207269217792, 10578455953408, 60716992766464, 262144000000000, 922190162669056, 2779905883635712, 7427658739644928, 18014398509481984, 40353607000000000, 84590643846578176, 167619550409708032, 316478381828866048, 572994802228616704
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016797, A016957, A016958, A016959, A016960, A016961, A016962, A016963, A016964.
Subsequence of A001017.

Programs

  • Magma
    [(6*n+4)^9: n in [0..20]]; // Vincenzo Librandi, May 07 2011
  • Mathematica
    (6*Range[0,20]+4)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{262144,1000000000,68719476736,1207269217792,10578455953408,60716992766464,262144000000000,922190162669056,2779905883635712,7427658739644928},20] (* Harvey P. Dale, Mar 04 2016 *)

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016957(n)^9 = A016958(n)^3.
a(n) = 2^9*A016797(n).
Sum_{n>=0} 1/a(n) = 9841*zeta(9)/10077696 - 809*Pi^9/(14285134080*sqrt(3)). (End)

A016966 a(n) = (6*n + 4)^10.

Original entry on oeis.org

1048576, 10000000000, 1099511627776, 26559922791424, 296196766695424, 2064377754059776, 10485760000000000, 42420747482776576, 144555105949057024, 430804206899405824, 1152921504606846976, 2824752490000000000, 6428888932339941376, 13744803133596058624
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016798, A016957, A016958, A016959, A016960, A016961, A016962, A016963, A016964, A016965.
Subsequence of A008454.

Programs

Formula

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016957(n)^10 = A016958(n)^5 = A016961(n)^2.
a(n) = 2^10*A016798(n).
Sum_{n>=0} 1/a(n) = PolyGamma(9, 2/3)/21941965946880. (End)

A016967 a(n) = (6*n + 4)^11.

Original entry on oeis.org

4194304, 100000000000, 17592186044416, 584318301411328, 8293509467471872, 70188843638032384, 419430400000000000, 1951354384207722496, 7516865509350965248, 24986644000165537792, 73786976294838206464, 197732674300000000000, 488595558857835544576, 1127073856954876807168
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016799, A016957, A016958, A016959, A016960, A016961, A016962, A016963, A016964, A016965, A016966.
Subsequence of A008455.

Programs

Formula

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016957(n)^11.
a(n) = 2^11*A016799(n).
Sum_{n>=0} 1/a(n) = 88573*zeta(11)/362797056 - 1847*Pi^11/(1285662067200*sqrt(3)). (End)

A016968 a(n) = (6*n + 4)^12.

Original entry on oeis.org

16777216, 1000000000000, 281474976710656, 12855002631049216, 232218265089212416, 2386420683693101056, 16777216000000000000, 89762301673555234816, 390877006486250192896, 1449225352009601191936, 4722366482869645213696, 13841287201000000000000, 37133262473195501387776
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A016800, A016957, A016958, A016959, A016960, A016961, A016962, A016963, A016964, A016965, A016966, A016967.
Subsequence of A008456.

Programs

Formula

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016957(n)^12 = A016958(n)^6 = A016959(n)^4 = A016960(n)^3 = A016962(n)^2.
a(n) = 2^12*A016800(n).
Sum_{n>=0} 1/a(n) = PolyGamma(11, 2/3)/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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