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 1-3 of 3 results.

A153819 Linear recurrence with a(n) = 3a(n-1) - a(n-2) + 2 = 4a(n-1) - 4a(n-2) + a(n-3). Full sequence for A153466.

Original entry on oeis.org

16, 34, 88, 232, 610, 1600, 4192, 10978, 28744, 75256, 197026, 515824, 1350448, 3535522, 9256120, 24232840, 63442402, 166094368, 434840704, 1138427746, 2980442536, 7802899864, 20428257058, 53481871312, 140017356880, 366570199330, 959693241112, 2512509524008
Offset: 0

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Author

Paul Curtz, Jan 02 2009

Keywords

Comments

a(n) mod 9 = 7.
A two-way infinite sequence with a(-n) = a(n-1).

Links

Programs

  • Magma
    [18*Fibonacci(2*n+1)-2: n in [0..30]]; // Vincenzo Librandi, Jun 19 2016
  • Mathematica
    LinearRecurrence[{4, -4, 1}, {16, 34, 88} , 100] (* G. C. Greubel, Jun 18 2016 *)
  • PARI
    Vec(2*(8-15*x+8*x^2)/((1-x)*(1-3*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 02 2016

Formula

G.f.: 2*(8-15*x+8*x^2)/((1-x)*(1-3*x+x^2)). - Jaume Oliver Lafont, Aug 30 2009
a(n) = 2*A153873(n) = 18*Fibonacci(2*n+1)-2.
a(n) = (2^(-n)*(-5*2^(1+n)-9*(3-sqrt(5))^n*(-5+sqrt(5))+9*(3+sqrt(5))^n*(5+sqrt(5))))/5. - Colin Barker, Nov 02 2016

Extensions

Edited by Charles R Greathouse IV, Oct 05 2009

A010727 Constant sequence: the all 7's sequence.

Original entry on oeis.org

7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

a(n) = A153466(n) mod 9. - Paul Curtz, Dec 27 2008
Continued fraction expansion of A176439. - Bruno Berselli, Mar 15 2011
Final digit of 16^(2^n) + 1. That is, the last digit of every Fermat number F(n) is 7, where n >= 2. - Arkadiusz Wesolowski, Jul 28 2011
Decimal expansion of 7/9. - Arkadiusz Wesolowski, Sep 12 2011

Links

Crossrefs

Cf. A000012 (the all 1's sequence), A153466, A176439.

Programs

Formula

G.f.: 7/(1-x). - Bruno Berselli, Mar 15 2011
a(n) = 7. - Arkadiusz Wesolowski, Sep 12 2011
E.g.f.: 7*e^x. - Vincenzo Librandi, Jan 28 2012

A179436 a(n) = (3*n+7)*(3*n+2)/2.

Original entry on oeis.org

7, 25, 52, 88, 133, 187, 250, 322, 403, 493, 592, 700, 817, 943, 1078, 1222, 1375, 1537, 1708, 1888, 2077, 2275, 2482, 2698, 2923, 3157, 3400, 3652, 3913, 4183, 4462, 4750, 5047, 5353, 5668, 5992, 6325, 6667, 7018, 7378, 7747, 8125, 8512, 8908, 9313, 9727, 10150
Offset: 0

Views

Author

Paul Curtz, Jan 12 2011

Keywords

Comments

Trisection of A055998.

Links

Crossrefs

Cf. A000217, A016777, A016789, A055998, A133694, A153466.

Programs

Formula

G.f.: (-7-4*x+2*x^2)/(x-1)^3.
a(n) = a(n-1) + 9*(n+1) = (14 + 27*n + 9*n^2)/2.
a(n) = 2*a(n-1) - a(n-2) + 9.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) mod 9 = A153466(n) mod 9 = 7.
Sum_{n>=0} 1/a(n) = 1/2-2*Pi*sqrt(3)/45 = 0.2581600... - R. J. Mathar, Apr 07 2011
a(n) = A133694(n+1) + 6*A000217(n+1). - Leo Tavares, Mar 24 2022
Sum_{n>=0} (-1)^n/a(n) = 3/10 - 4*log(2)/15. - Amiram Eldar, Mar 27 2022
From Elmo R. Oliveira, Oct 30 2024: (Start)
E.g.f.: exp(x)*(7 + 18*x + 9*x^2/2).
a(n) = A016777(n+2)*A016789(n)/2. (End)
Showing 1-3 of 3 results.

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

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