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 1-5 of 5 results.

A199773 y-values in the solution to 17*x^2 - 16 = y^2.

Original entry on oeis.org

1, 16, 103, 169, 1072, 6799, 11153, 70736, 448631, 735929, 4667504, 29602847, 48560161, 307984528, 1953339271, 3204234697, 20322311344, 128890789039, 211430929841, 1340964564176, 8504838737303, 13951237134809, 88483338924272, 561190465872959, 920570219967553
Offset: 1

Views

Author

Sture Sjöstedt, Nov 10 2011

Keywords

Comments

When are both n+1 and 17*n+1 perfect squares? This problem gives the equation 17*x^2-16=y^2.

Examples

			a(7) = 66*169-1 = 11153.

Links

Crossrefs

Cf. A199772, A199774, A199798.

Programs

  • Magma
    I:=[1,16,103,169,1072,6799]; [n le 6 select I[n] else 66*Self(n-3)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, Jan 06 2016
  • Mathematica
    LinearRecurrence[{0,0,66,0,0,-1}, {1,16,103,169,1072,6799}, 50]
CoefficientList[Series[(x + 1) (x^4 + 15 x^3 + 88 x^2 + 15 x + 1) / (x^6 - 66 x^3 + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 06 2016 *)
  • PARI
    Vec(x*(x+1)*(x^4+15*x^3+88*x^2+15*x+1)/(x^6-66*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Formula

a(n) = 66*a(n-3) - a(n-6), a(1)=1, a(2)=16, a(3)=103, a(4)=169, a(5)=1072, a(6)=6799.
G.f.: x*(x+1)*(x^4+15*x^3+88*x^2+15*x+1) / (x^6-66*x^3+1). - Colin Barker, Sep 01 2013

Extensions

More terms from T. D. Noe, Nov 10 2011

A199772 x-values in the solution to 17*x^2 - 16 = y^2.

Original entry on oeis.org

1, 4, 25, 41, 260, 1649, 2705, 17156, 108809, 178489, 1132036, 7179745, 11777569, 74697220, 473754361, 777141065, 4928884484, 31260608081, 51279532721, 325231678724, 2062726378985, 3383672018521, 21460361911300, 136108680404929, 223271073689665
Offset: 1

Views

Author

Sture Sjöstedt, Nov 10 2011

Keywords

Comments

When are both n+1 and 17*n+1 perfect squares? This problem gives the equation 17*x^2-16=y^2.

Examples

			a(7) = 66*41-1 = 2705.

Links

Crossrefs

Cf. A199773, A199774, A199798.

Programs

  • Mathematica
    LinearRecurrence[{0,0,66,0,0,-1}, {1,4,25,41,260,1649}, 50]
  • PARI
    Vec(-x*(x-1)*(x^4+5*x^3+30*x^2+5*x+1)/(x^6-66*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Formula

a(n) = 66*a(n-3) - a(n-6), a(1)=1, a(2)=4, a(3)=25, a(4)=41, a(5)=260, a(6)=1649.
G.f.: -x*(x-1)*(x^4+5*x^3+30*x^2+5*x+1) / (x^6-66*x^3+1). - Colin Barker, Sep 01 2013

Extensions

More terms from T. D. Noe, Nov 10 2011

A199798 y-values in the solution to 17*x^2 + 16 = y^2.

Original entry on oeis.org

4, 13, 21, 132, 837, 1373, 8708, 55229, 90597, 574596, 3644277, 5978029, 37914628, 240467053, 394459317, 2501790852, 15867181221, 26028336893, 165080281604, 1046993493533, 1717475775621, 10892796795012, 69085703391957, 113327372854093, 718759508189188
Offset: 1

Views

Author

Sture Sjöstedt, Nov 10 2011

Keywords

Comments

When are both n-1 and 17*n-1 perfect squares? This problem gives the equation 17*x^2+16=y^2.

Examples

			a(7)=66*132-4=8708.

Links

Crossrefs

Cf. A199774, A199772, A199773.

Programs

  • Mathematica
    LinearRecurrence[{0,0,66,0,0,-1}, {4,13,21,132,837,1373}, 50]
  • PARI
    Vec(-x*(13*x^5+21*x^4+132*x^3-21*x^2-13*x-4)/(x^6-66*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Formula

a(n) = 66*a(n-3) - a(n-6), a(1)=4, a(2)=13, a(3)=21, a(4)=132, a(5)=837, a(6)=1373.
G.f.: -x*(13*x^5+21*x^4+132*x^3-21*x^2-13*x-4) / (x^6-66*x^3+1). - Colin Barker, Sep 01 2013

Extensions

More terms from T. D. Noe, Nov 10 2011

A200409 The y-values in the solution to 19*x^2 - 18 = y^2.

Original entry on oeis.org

1, 39, 571, 911, 13299, 194141, 309739, 4521621, 66007369, 105310349, 1537337841, 22442311319, 35805208921, 522690344319, 7630319841091, 12173665722791, 177713179730619, 2594286303659621, 4139010540540019, 60421958418066141, 882049712924430049
Offset: 1

Views

Author

Sture Sjöstedt, Nov 17 2011

Keywords

Comments

When are both n+1 and 19*n+1 perfect squares? This gives the equation 19*x^2 - 18 = y^2.

Examples

			a(7) = 340*911 - 1 = 309739.

Links

Crossrefs

Cf. A200407, A199773, A199774, A199798.

Programs

  • Magma
    I:=[1, 39, 571, 911, 13299, 194141]; [n le 6 select I[n] else 340*Self(n-3)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, Nov 18 2011
  • Mathematica
    LinearRecurrence[{0, 0, 340, 0, 0, -1}, {1, 39, 571, 911, 13299,194141}, 50]
  • PARI
    Vec(x*(x+1)*(x^4+38*x^3+533*x^2+38*x+1)/(x^6-340*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Formula

a(n) = 340*a(n-3) - a(n-6), a(1)=1, a(2)=39, a(3)=571, a(4)=911, a(5)=13299, a(6)=194141.
G.f.: x*(x+1)*(x^4 + 38*x^3 + 533*x^2 + 38*x + 1) / (x^6 - 340*x^3 + 1). - Colin Barker, Sep 01 2013

A200407 The x-values in the solution to 19*x^2 - 18 = y^2.

Original entry on oeis.org

1, 9, 131, 209, 3051, 44539, 71059, 1037331, 15143129, 24159851, 352689489, 5148619321, 8214278281, 119913388929, 1750515426011, 2792830455689, 40770199546371, 595170096224419, 949554140655979, 13861747932377211, 202356082200876449, 322845614992577171
Offset: 1

Views

Author

Sture Sjöstedt, Nov 17 2011

Keywords

Comments

When are both n+1 and 19*n+1 perfect squares? This gives the equation 19*x^2-18=y^2.

Examples

			a(7)=340*209-1=71059.

Links

Crossrefs

Cf. A199773, A199774, A199798, A200409.

Programs

  • Mathematica
    LinearRecurrence[{0, 0, 340, 0, 0, -1}, {1, 9, 131, 209, 3051, 44539}, 50]
  • PARI
    Vec(-x*(x-1)*(x^4+10*x^3+141*x^2+10*x+1)/(x^6-340*x^3+1) + O(x^100)) \\ Colin Barker, Sep 01 2013

Formula

a(n) = 340*a(n-3)+a(n-6), a(1)=1, a(2)=9, a(3)=131, a(4)=209, a(5)=3051, a(6)=44539.
G.f.: -x*(x-1)*(x^4+10*x^3+141*x^2+10*x+1) / (x^6-340*x^3+1). - Colin Barker, Sep 01 2013
Showing 1-5 of 5 results.

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