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.

User: Andreas Rieber

Andreas Rieber's wiki page.

Andreas Rieber has authored 4 sequences.

A220089 a(n) = 2^n - 243.

Original entry on oeis.org

-242, -241, -239, -235, -227, -211, -179, -115, 13, 269, 781, 1805, 3853, 7949, 16141, 32525, 65293, 130829, 261901, 524045, 1048333, 2096909, 4194061, 8388365, 16776973, 33554189, 67108621, 134217485, 268435213, 536870669, 1073741581, 2147483405, 4294967053
Offset: 0

Views

Author

Andreas Rieber, Dec 04 2012

Keywords

Links

Crossrefs

Cf. A000225, A036563, A185346, A220087, A220088.

Programs

  • Mathematica
    Table[2^n - 243, {n, 0, 40}] (* T. D. Noe, Dec 04 2012 *)

Formula

From Chai Wah Wu, Jan 17 2020: (Start)
a(n) = 3*a(n-1) - 2*a(n-2) for n > 1.
G.f.: (485*x - 242)/((x - 1)*(2*x - 1)). (End)
From Elmo R. Oliveira, Nov 11 2023: (Start)
a(n) = 2*a(n-1) + 243 with a(0) = -242.
E.g.f.: exp(2*x) - 243*exp(x). (End)

A220088 a(n) = 2^n - 81.

Original entry on oeis.org

-80, -79, -77, -73, -65, -49, -17, 47, 175, 431, 943, 1967, 4015, 8111, 16303, 32687, 65455, 130991, 262063, 524207, 1048495, 2097071, 4194223, 8388527, 16777135, 33554351, 67108783, 134217647, 268435375, 536870831, 1073741743, 2147483567, 4294967215
Offset: 0

Views

Author

Andreas Rieber, Dec 04 2012

Keywords

Links

Crossrefs

Cf. A000225, A036563, A185346, A220087.

Programs

  • Mathematica
    Table[2^n - 81, {n, 0, 40}] (* T. D. Noe, Dec 04 2012 *)

Formula

From Chai Wah Wu, Jan 17 2020: (Start)
a(n) = 3*a(n-1) - 2*a(n-2) for n > 1.
G.f.: (161*x - 80)/((x - 1)*(2*x - 1)). (End)
From Elmo R. Oliveira, Nov 11 2023: (Start)
a(n) = 2*a(n-1) + 81 with a(0) = -80.
E.g.f.: exp(2*x) - 81*exp(x). (End)

A220087 a(n) = 2^n - 27.

Original entry on oeis.org

-26, -25, -23, -19, -11, 5, 37, 101, 229, 485, 997, 2021, 4069, 8165, 16357, 32741, 65509, 131045, 262117, 524261, 1048549, 2097125, 4194277, 8388581, 16777189, 33554405, 67108837, 134217701, 268435429, 536870885, 1073741797, 2147483621, 4294967269
Offset: 0

Views

Author

Andreas Rieber, Dec 04 2012

Keywords

Links

Crossrefs

Cf. A000225, A036563, A185346.

Programs

  • Mathematica
    Table[2^n - 27, {n, 0, 40}] (* T. D. Noe, Dec 04 2012 *)
LinearRecurrence[{3,-2},{-26,-25},40] (* Harvey P. Dale, May 17 2018 *)

Formula

From Chai Wah Wu, Jan 17 2020: (Start)
a(n) = 3*a(n-1) - 2*a(n-2) for n > 1.
G.f.: (53*x - 26)/((x - 1)*(2*x - 1)). (End)
From Elmo R. Oliveira, Nov 08 2023: (Start)
a(n) = 2*a(n-1) + 27 with a(0) = -26.
E.g.f.: exp(2*x) - 27*exp(x). (End)

A185346 a(n) = 2^n - 9.

Original entry on oeis.org

-8, -7, -5, -1, 7, 23, 55, 119, 247, 503, 1015, 2039, 4087, 8183, 16375, 32759, 65527, 131063, 262135, 524279, 1048567, 2097143, 4194295, 8388599, 16777207, 33554423, 67108855, 134217719, 268435447, 536870903, 1073741815, 2147483639, 4294967287, 8589934583
Offset: 0

Views

Author

Andreas Rieber, Dec 04 2012

Keywords

Links

Crossrefs

Cf. A000225, A036563, A172252 (essentially the same).

Programs

Formula

G.f.: ( -8+17*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Dec 17 2012
E.g.f.: exp(2*x) - 9*exp(x). - G. C. Greubel, Jun 28 2017
From Elmo R. Oliveira, Nov 08 2023: (Start)
a(n) = 2*a(n-1) + 9 with a(0) = -8.
a(n) = 3*a(n-1) - 2*a(n-2) for n > 1. (End)

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