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.

A173697 a(n) = ceiling(A013984(n)/2).

Original entry on oeis.org

1, 0, 1, 1, 1, 2, 3, 4, 6, 10, 16, 25, 40, 63, 100, 159, 253, 402, 640, 1017, 1617, 2570, 4087, 6498, 10331, 16427, 26118, 41528, 66030, 104988, 166931, 265421, 422020, 671014, 1066916, 1696402, 2697289, 4288703, 6819061, 10842344, 17239385, 27410714, 43583183, 69297495, 110183389, 175192180, 278556508
Offset: 0

Views

Author

Roger L. Bagula, Nov 25 2010

Keywords

Links

Crossrefs

Cf. A013984.

Programs

  • Mathematica
    Ceiling[CoefficientList[Series[1/(1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7), {x, 0, 50}], x]/2] (* G. C. Greubel, Nov 23 2016 *)

Formula

a(n) = ceiling(A013984(n)/2).

Extensions

Erroneous leading zeros deleted by G. C. Greubel, Nov 23 2016

A107479 a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7).

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 12, 20, 31, 50, 79, 126, 200, 318, 506, 804, 1279, 2033, 3233, 5140, 8173, 12995, 20662, 32853, 52236, 83056, 132059, 209975, 333861, 530841, 844040, 1342028, 2133832, 3392804, 5394577, 8577406, 13638122, 21684687, 34478769
Offset: 0

Views

Author

Roger L. Bagula, May 27 2005

Keywords

Links

Crossrefs

Cf. A013984.
Cf. A107480, A109538, A109543, A109544, A114749, A125950, A130844, A143335, A147851.

Programs

  • Magma
    m:=50; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1+x)*(1+x+x^2)*(x^2-x+1)/(1-x^2-x^3-x^4-x^5-x^6-x^7) )); // G. C. Greubel, Nov 03 2018
  • Mathematica
    LinearRecurrence[{0,1,1,1,1,1,1}, {0,1,1,2,3,5,8}, 40] (* Harvey P. Dale, Sep 26 2012 *)
CoefficientList[Series[x (1 + x) (1 + x + x^2) (x^2 - x + 1)/(1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 16 2014 *)
  • PARI
    concat(0, Vec(x*(1+x)*(1+x+x^2)*(x^2-x+1)/(1-x^2-x^3-x^4-x^5-x^6-x^7) + O(x^60))) \\ Michel Marcus, Oct 16 2014

Formula

Lim_{n->infinity} a(n)/a(n-1) = 1.5900053739...
G.f.: x*(1 + x)*(1 - x + x^2)*(1 + x + x^2)/(1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7).

Extensions

Definition replaced by recurrence - The Associate Editors of the OEIS, Oct 02 2009
Spelling and formatting corrected, index link added - Charles R Greathouse IV, Jan 26 2011

A107480 a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-7).

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 14, 25, 42, 71, 121, 207, 353, 601, 1025, 1748, 2980, 5080, 8661, 14767, 25176, 42922, 73178, 124762, 212707, 362644, 618273, 1054096, 1797131, 3063933, 5223708, 8905915, 15183719, 25886764, 44134416, 75244889, 128285220, 218713827
Offset: 0

Views

Author

Roger L. Bagula, May 27 2005

Keywords

Comments

Lim_{n->infinity} a(n)/a(n-1) = 1.70490277..., the real root of x^5 = x^4 + x^3 + 1.

Links

Crossrefs

Cf. A013984.
Cf. A107479, A109538, A109543, A109544, A114749, A125950, A130844, A143335, A147851.

Programs

  • Magma
    m:=40; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1 +x^2-x^5)/((1+x^2)*(1-x-x^2-x^5)))); // G. C. Greubel, Nov 03 2018
  • Mathematica
    LinearRecurrence[{1,0,1,1,1,0,1}, {0,1,1,2,3,5,8}, 50] (* Harvey P. Dale, May 21 2012 *)
  • PARI
    concat([0], Vec(x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)) + O(x^40))) \\ Colin Barker, Dec 17 2017

Formula

G.f.: x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)). - Colin Barker, Dec 17 2017

Extensions

Entry rewritten by Charles R Greathouse IV, Jan 26 2011
Showing 1-3 of 3 results.

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