A145123 -id:A145123 - cp's OEIS frontend

A145124 Numbers x such that there exists n in N : (x+1)^3-x^3=19*n^2.

2, 757, 228762, 69085517, 20863597522, 6300737366277, 1902801821018282, 574639849210155037, 173539331659645803042, 52408303521363822363797, 15827134124120214708063802, 4779742097180783478012904557, 1443466286214472490145189112562

Offset: 1

Richard Choulet, Oct 02 2008

			a(1)=2 because 3^3-2^3=19*1.

Index entries for linear recurrences with constant coefficients, signature (303,-303,1).

Cf. A145123.

CoefficientList[Series[(-2 - 151*x + 3*x^2)/((x - 1)*(x^2 - 302*x + 1)), {x, 0, 15}], x] (* Wesley Ivan Hurt, Sep 04 2022 *)

Vec(x*(-2-151*x+3*x^2)/((x-1)*(x^2-302*x+1)) + O(x^30)) \\ Colin Barker, Oct 18 2014

a(n+2) = 302*a(n+1)-a(n)+150.

G.f.: x*(-2-151*x+3*x^2) / ( (x-1)*(x^2-302*x+1) ). - R. J. Mathar, Nov 27 2011

Editing and more terms from Colin Barker, Oct 18 2014

A145120 Numbers X such that (X^2-19)/57 is a square.

Original entry on oeis.org

38, 11438, 3454238, 1043168438, 315033414038, 95139047871038, 28731677423639438, 8676871442891239238, 2620386444075730610438, 791348029239427753113038, 238984484443863105709527038

Offset: 1

Richard Choulet, Oct 02 2008

			a(1)=38 because 38^2 = 57*25+19.

Index entries for linear recurrences with constant coefficients, signature (302,-1).

LinearRecurrence[{302,-1},{38,11438},20] (* Harvey P. Dale, Jan 24 2013 *)

a(n) = 302*a(n-1) - a(n-2).
From R. J. Mathar, Nov 27 2011: (Start)
G.f.: -38*x*(-1+x) / ( 1-302*x+x^2 ).
a(n) = 38*A145123(n). (End)

A145121 Numbers n such that there exists x in N : (x+19)^3-x^3=n^2.

Original entry on oeis.org

361, 108661, 32815261, 9910100161, 2992817433361, 903820954774861, 272950935524574661, 82430278707466772761, 24893671218719440799161, 7517806277774563654573861, 2270352602216699504240506861, 685638968063165475716978498161, 207060698002473756967023265937761

Offset: 1

Richard Choulet, Oct 02 2008

			a(1)=361 because 57^3-38^3=361^2.

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (302,-1).

I:=[361,108661]; [n le 2 select I[n] else 302*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 19 2014

CoefficientList[Series[361 (1 - x)/(x^2 - 302 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 19 2014 *)

Vec(-361*x*(x-1)/(x^2-302*x+1) + O(x^20)) \\ Colin Barker, Oct 19 2014

a(n+2) = 302*a(n+1)-a(n).
a(n) = 361*A145123(n). - Colin Barker, Oct 19 2014
G.f.: -361*x*(x-1) / (x^2-302*x+1). - Colin Barker, Oct 19 2014

Editing and more terms from Colin Barker, Oct 19 2014

cp's OEIS Frontend

A145124 Numbers x such that there exists n in N : (x+1)^3-x^3=19*n^2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A145120 Numbers X such that (X^2-19)/57 is a square.

Views

Author

Keywords

Examples

Links

Programs

Mathematica

Formula

A145121 Numbers n such that there exists x in N : (x+19)^3-x^3=n^2.

Views

Author

Keywords

Examples

Links

Programs

Magma

Mathematica

PARI

Formula

Extensions