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

A199774 x-values in the solution to 17*x^2 + 16 = y^2.

Original entry on oeis.org

0, 3, 5, 32, 203, 333, 2112, 13395, 21973, 139360, 883867, 1449885, 9195648, 58321827, 95670437, 606773408, 3848356715, 6312798957, 40037849280, 253933221363, 416549060725, 2641891279072, 16755744253243, 27485925208893, 174324786569472, 1105625187492675
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*32-0=2112.

Links

Crossrefs

Cf. A199772, A199773, A199798.

Programs

  • Mathematica
    LinearRecurrence[{0,0,66,0,0,-1}, {0,3,5,32,203,333}, 50]
  • PARI
    Vec(x^2*(3*x^4+5*x^3+32*x^2+5*x+3)/(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)=0, a(2)=3, a(3)=5, a(4)=32, a(5)=203, a(6)=333.
G.f.: x^2*(3*x^4+5*x^3+32*x^2+5*x+3) / (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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