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.

A097335 a(n) = Sum_{k=0..n} C(n-k, floor(k/2))*3^k.

Original entry on oeis.org

1, 4, 4, 13, 49, 85, 202, 643, 1408, 3226, 9013, 21685, 50719, 131836, 327001, 783472, 1969996, 4913005, 11964253, 29694217, 73911262, 181589539, 448837492, 1114038850, 2748344701, 6787882129, 16814231779, 41549334088, 102640273249
Offset: 0

Views

Author

Paul Barry, Aug 05 2004

Keywords

Links

Crossrefs

Cf. A097333, A097334, A097336.

Formula

G.f. : (1+3x)/(1-x-9x^3); a(n)=a(n-1)+9a(n-3).

A097336 Sum k=0..n, C(n-k, floor(k/2))4^k.

Original entry on oeis.org

1, 5, 5, 21, 101, 181, 517, 2133, 5029, 13301, 47429, 127893, 340709, 1099573, 3145861, 8597205, 26190373, 76524149, 214079429, 633125397, 1857511781, 5282782645, 15412788997, 45132977493, 129657499813, 376262123765
Offset: 0

Views

Author

Paul Barry, Aug 05 2004

Keywords

Comments

The sequence sum{k=0..n, C(n-k,floor(k/2))r^k} has g.f. (1+rx)/(1-x-r^2x^3).

Links

Crossrefs

Cf. A097333, A097334, A097335.

Programs

  • Mathematica
    LinearRecurrence[{1,0,16},{1,5,5},30] (* Harvey P. Dale, Sep 15 2011 *)

Formula

G.f. : (1+4x)/(1-x-16x^3); a(n)=a(n-1)+16a(n-3).

A098581 Expansion of (1+2*x+4*x^2)/(1-x-8*x^4).

Original entry on oeis.org

1, 3, 7, 7, 15, 39, 95, 151, 271, 583, 1343, 2551, 4719, 9383, 20127, 40535, 78287, 153351, 314367, 638647, 1264943, 2491751, 5006687, 10115863, 20235407, 40169415, 80222911, 161149815, 323033071, 644388391, 1286171679, 2575370199
Offset: 0

Views

Author

Paul Barry, Sep 16 2004

Keywords

Links

Crossrefs

Cf. A078467, A097334.

Programs

  • Magma
    I:=[1,3,7,7]; [n le 4 select I[n] else Self(n-1) + 8*Self(n-4): n in [1..30]]; // G. C. Greubel, Feb 03 2018
  • Mathematica
    CoefficientList[Series[(1+2x+4x^2)/(1-x-8x^4),{x,0,40}],x] (* or *) LinearRecurrence[{1,0,0,8},{1,3,7,7},40] (* Harvey P. Dale, Feb 04 2015 *)
  • PARI
    x='x+O('x^30); Vec((1+2*x+4*x^2)/(1-x-8*x^4)) \\ G. C. Greubel, Feb 03 2018

Formula

a(n) = a(n-1) + 8*a(n-4).
a(n) = Sum_{k=0..n} binomial(n-k, floor(k/3)) * 2^k.
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.