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 1-2 of 2 results.

A077833 Expansion of 1/(1-2*x-3*x^2-2*x^3).

Original entry on oeis.org

1, 2, 7, 22, 69, 218, 687, 2166, 6829, 21530, 67879, 214006, 674709, 2127194, 6706527, 21144054, 66662077, 210169370, 662613079, 2089058422, 6586294821, 20764991066, 65466983439, 206401529718, 650733991885, 2051606539802, 6468218114695, 20392723832566
Offset: 0

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Author

N. J. A. Sloane, Nov 17 2002

Keywords

Links

Crossrefs

Partial sums of S(n, x), x=1..19 see A077832 and A-number references.
First differences of A077826.

Programs

  • Mathematica
    CoefficientList[Series[1/(1-2x-3x^2-2x^3),{x,0,30}],x] (* or *) LinearRecurrence[{2,3,2},{1,2,7},30] (* Harvey P. Dale, Sep 07 2017 *)
  • PARI
    Vec(1/(1-2*x-3*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

A250128 Number of triforces generated at iteration n in a Koch-Sierpiński Ninja Star.

Original entry on oeis.org

0, 1, 3, 9, 30, 96, 309, 996, 3207, 10329, 33267, 107142, 345072, 1111371, 3579384, 11528097, 37128459, 119579361, 385128390, 1240380240, 3994883733
Offset: 0

Views

Author

Kyle M. Zimmer, Nov 12 2014

Keywords

Comments

This sequence describes the number of triangles produced in each iteration of the fractal that is generated by nesting two-dimensional trees of valency three inside one another geometrically.

Links

Programs

  • Java
    // See links.

Formula

Refer to the blog link.
Conjecture: a(n) = 2*a(n-1) + 3*a(n-2) + 3*a(n-3). - Colin Barker, Nov 13 2014
Empirical g.f.: -x*(x+1) / (3*x^3 + 3*x^2 + 2*x - 1). - Colin Barker, Nov 13 2014
Empirical: a(n) = A077832(n-2) + A077832(n-1). - R. J. Mathar, May 21 2018
Showing 1-2 of 2 results.

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

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