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 1-6 of 6 results.

A017020 a(n) = (7*n + 3)^4.

Original entry on oeis.org

81, 10000, 83521, 331776, 923521, 2085136, 4100625, 7311616, 12117361, 18974736, 28398241, 40960000, 57289761, 78074896, 104060401, 136048896, 174900625, 221533456, 276922881, 342102016, 418161601
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A017017, A017018, A017019, A017021 - A017028.

Programs

  • Magma
    [(7*n+3)^4: n in [0..35]]; // Vincenzo Librandi, Jul 14 2011
  • Mathematica
    (7*Range[0,20]+3)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1},{81,10000,83521,331776,923521},30] (* Harvey P. Dale, Oct 29 2019 *)
  • SageMath
    [(7*n+3)^4 for n in range(41)] # G. C. Greubel, Oct 17 2023

Formula

From G. C. Greubel, Oct 17 2023: (Start)
G.f.: (81 + 9595*x + 34331*x^2 + 13361*x^3 + 256*x^4)/(1 - x)^5.
E.g.f.: (81 + 9919*x + 31801*x^2 + 18522*x^3 + 2401*x^4)*exp(x). (End)

A017021 a(n) = (7*n + 3)^5.

Original entry on oeis.org

243, 100000, 1419857, 7962624, 28629151, 79235168, 184528125, 380204032, 714924299, 1252332576, 2073071593, 3276800000, 4984209207, 7339040224, 10510100501, 14693280768, 20113571875, 27027081632, 35723051649, 46525874176
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A017017 - A017020, A017022 - A017028.

Programs

  • Magma
    [(7*n+3)^5: n in [0..35]]; // Vincenzo Librandi, Jul 14 2011
  • Mathematica
    (7*Range[0,20]+3)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{243,100000,1419857,7962624,28629151,79235168},20] (* Harvey P. Dale, Aug 27 2017 *)
  • SageMath
    [(7*n+3)^5 for n in range(41)] # G. C. Greubel, Oct 17 2023

Formula

From G. C. Greubel, Oct 17 2023: (Start)
G.f.: (243 + 98542*x + 823502*x^2 + 938622*x^3 + 154907*x^4 + 1024*x^5)/(1-x)^6.
E.g.f.: (243 + 99757*x + 610050*x^2 + 667135*x^3 + 204085*x^4 + 16807*x^5)*exp(x). (End)
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Wesley Ivan Hurt, Jun 26 2025

A017022 a(n) = (7*n + 3)^6.

Original entry on oeis.org

729, 1000000, 24137569, 191102976, 887503681, 3010936384, 8303765625, 19770609664, 42180533641, 82653950016, 151334226289, 262144000000, 433626201009, 689869781056, 1061520150601, 1586874322944
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A017017 - A017021, A017023 - A017028.

Programs

Formula

From G. C. Greubel, Oct 17 2023: (Start)
G.f.: (729 + 994897*x + 17152878*x^2 + 43114478*x^3 + 21697313*x^4 + 1742889*x^5 + 4096*x^6)/(1-x)^7.
E.g.f.: (729 + 999271*x + 11069149*x^2 + 20281590*x^3 + 10996580*x^4 + 2067261*x^5 + 117649*x^6)*exp(x). (End)

A017023 a(n) = (7*n + 3)^7.

Original entry on oeis.org

2187, 10000000, 410338673, 4586471424, 27512614111, 114415582592, 373669453125, 1028071702528, 2488651484819, 5455160701056, 11047398519097, 20971520000000, 37725479487783, 64847759419264
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A017017 - A017022, A017024 - A017028.

Programs

  • Magma
    [(7*n+3)^7: n in [0..30]]; // Vincenzo Librandi, Jul 14 2011
  • Mathematica
    (7*Range[0,30]+3)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28, 8,-1}, {2187,10000000,410338673,4586471424,27512614111,114415582592, 373669453125,1028071702528}, 30] (* Harvey P. Dale, Jul 07 2020 *)
  • SageMath
    [(7*n+3)^7 for n in range(41)] # G. C. Greubel, Oct 17 2023

Formula

From G. C. Greubel, Oct 17 2023: (Start)
G.f.: (2187 + 9982504*x + 330399909*x^2 + 1583639568*x^3 + 1750478653*x^4 + 456781416*x^5 + 19356099*x^6 + 16384*x^7)/(1-x)^8.
E.g.f.: (2187 + 9997813*x + 195170430*x^2 + 564242203*x^3 + 482865110*x^4 + 155531978*x^5 + 19765032*x^6 + 823543*x^7)*exp(x). (End)

A017019 a(n) = (7*n + 3)^3.

Original entry on oeis.org

27, 1000, 4913, 13824, 29791, 54872, 91125, 140608, 205379, 287496, 389017, 512000, 658503, 830584, 1030301, 1259712, 1520875, 1815848, 2146689, 2515456, 2924207, 3375000, 3869893, 4410944, 5000211
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A017017, A017018, A017020 - A017028.

Programs

Formula

From G. C. Greubel, Oct 17 2023: (Start)
G.f.: (27 + 892*x + 1075*x^2 + 64*x^3)/(1 - x)^4.
E.g.f.: (27 + 973*x + 1470*x^2 + 343*x^3)*exp(x). (End)

A017024 a(n) = (7*n + 3)^8.

Original entry on oeis.org

6561, 100000000, 6975757441, 110075314176, 852891037441, 4347792138496, 16815125390625, 53459728531456, 146830437604321, 360040606269696, 806460091894081, 1677721600000000, 3282116715437121, 6095689385410816
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A017017 - A017023, A017025 - A017028.

Programs

Formula

From G. C. Greubel, Oct 17 2023: (Start)
G.f.: (6561 +99940951*x +6075993637*x^2 +50892946083*x^3 +104941304419*x^4 +61119660133*x^5 +9093089943*x^6 +213769057*x^7 +65536*x^8)/(1-x)^9.
E.g.f.: (6561 +99993439*x +3387882001*x^2 +14908005882*x^3 +18918513831*x^4 +9290270934*x^5 +1978150286*x^6 +181179460*x^7 +5764801*x^8)*exp(x). (End)
Showing 1-6 of 6 results.

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

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