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.

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A155196 a(n)=7*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=6, a(2)=42 .

Original entry on oeis.org

1, 6, 42, 300, 2142, 15294, 109200, 779694, 5567058, 39749100, 283810758, 2026424406, 14468781600, 103307895606, 737624050842, 5266676251500, 37604357811342, 268497180930894, 1917084624327600, 13688089551224094
Offset: 0

Views

Author

Philippe Deléham, Jan 21 2009

Keywords

Programs

  • Mathematica
    Join[{1},LinearRecurrence[{7,1},{6,42},20]] (* Harvey P. Dale, Sep 04 2014 *)

Formula

G.f.: (1-x-x^2)/(1-7*x-x^2).
a(n) = Sum_{k, 0<=k<=n} A155161(n,k)*6^k. - Philippe Deléham, Feb 08 2012

A155197 a(n) = 8*a(n-1) + a(n-2) for n>2, with a(0)=1, a(1)=7, a(2)=56.

Original entry on oeis.org

1, 7, 56, 455, 3696, 30023, 243880, 1981063, 16092384, 130720135, 1061853464, 8625547847, 70066236240, 569155437767, 4623309738376, 37555633344775, 305068376496576, 2478102645317383, 20129889539035640, 163517218957602503
Offset: 0

Views

Author

Philippe Deléham, Jan 21 2009

Keywords

Crossrefs

Cf. A155161.

Programs

  • Maple
    a:=proc(n) option remember; if n=0 then 1 elif n=1 then 7 elif n=2 then 56 else 8*a(n-1)+a(n-2); fi; end: seq(a(n), n=0..30); # Wesley Ivan Hurt, Jan 28 2017
  • Mathematica
    LinearRecurrence[{8, 1}, {1, 7, 56}, 20] (* or *)
    CoefficientList[Series[(1 - x - x^2)/(1 - 8 x - x^2), {x, 0, 19}], x] (* or *)
    {1, 7}~Join~Table[Simplify[# (14/17) ((4 + #)^n - (4 - #)^n) + (7/2) ((4 + #)^n + (4 - #)^n) + Mod[Binomial[2 n, n], 2]] &@ Sqrt@ 17, {n, 18}] (* Michael De Vlieger, Jan 30 2017 *)

Formula

G.f.: (1-x-x^2)/(1-8*x-x^2).
a(n) = Sum_{k=0..n} A155161(n,k)*7^k. - Philippe Deléham, Feb 08 2012

A155198 a(n)=9*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=8, a(2)=72 .

Original entry on oeis.org

1, 8, 72, 656, 5976, 54440, 495936, 4517864, 41156712, 374928272, 3415511160, 31114528712, 283446269568, 2582130954824, 23522624862984, 214285754721680, 1952094417358104, 17783135510944616, 162000314015859648
Offset: 0

Views

Author

Philippe Deléham, Jan 21 2009

Keywords

Programs

  • Mathematica
    LinearRecurrence[{9,1},{1,8,72},20] (* Harvey P. Dale, Aug 22 2016 *)

Formula

G.f.: (1-x-x^2)/(1-9*x-x^2).
a(n) = Sum_{k, 0<=k<=n} A155161(n,k)*8^k. - Philippe Deléham, Feb 08 2012

A155199 a(n) = 10*a(n-1) + a(n-2), n > 2 ; a(0) = 1, a(1) = 9, a(2) = 90.

Original entry on oeis.org

1, 9, 90, 909, 9180, 92709, 936270, 9455409, 95490360, 964359009, 9739080450, 98355163509, 993290715540, 10031262318909, 101305913904630, 1023090401365209, 10332209927556720, 104345189676932409, 1053784106696880810, 10642186256645740509, 107475646673154285900
Offset: 0

Views

Author

Philippe Deléham, Jan 21 2009

Keywords

Crossrefs

Programs

  • Mathematica
    LinearRecurrence[{10,1},{1,9,90},20] (* Harvey P. Dale, Dec 20 2022 *)

Formula

G.f.: (1 - x - x^2)/(1 - 10*x - x^2).
a(n) = Sum_{k=0..n} A155161(n,k)*9^k. - Philippe Deléham, Feb 08 2012
E.g.f.: 1 + 9*exp(5*x)*sinh(sqrt(26)*x)/sqrt(26). - Stefano Spezia, Mar 01 2023
Previous Showing 11-14 of 14 results.