A201225 Values x for infinite sequence x^3-y^2 = d with decreasing coefficient r=sqrt(x)/d which tend to 1/(1350*sqrt(5))or infinity family of solutions Mordell curve with extension sqrt(5).

6100, 2305180, 748476100, 241118603980, 77641444770100, 25000340035616380, 8050032494909496100, 2592085474592828222380, 834643472994047002110100, 268752606222334691877221980, 86537504560185639786707316100, 27864807715774753485364243735180

Offset

1,1

Comments

a(1) = A200656(4) = A201047(4).

a(2) = A200656(36) = A201047(26).

All points in this sequence are extremal points (definition see A200656) and from these reason is subset of A200656 and primary (definition see A200656) and from these reason is subset of A201047.

Links

Table of n, a(n) for n=1..12.

Index entries for linear recurrences with constant coefficients, signature (341,-6138,6138,-341,1).

Formula

G.f.: z*(20*(-305-11254*z+7424*z^2-346*z^3+z^4))/((-1+z)*(1- 322*z+z^2)*(1-18*z+z^2)).

a(n) = 341*a(n-1) - 6138*a(n-2) + 6138*a(n-3) - 341*a(n-4) + a(n-5).

Mathematica

LinearRecurrence[{341, -6138, 6138, -341, 1}, {6100, 2305180, 748476100, 241118603980, 77641444770100}, 20] (* Harvey P. Dale, Aug 17 2016 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -341, 6138, -6138, 341]^(n-1)*[6100; 2305180; 748476100; 241118603980; 77641444770100])[1, 1] \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Cf. A200216, A200656, A201047.

Sequence in context: A236824 A211929 A251994 * A031619 A235764 A235547

Adjacent sequences: A201222 A201223 A201224 * A201226 A201227 A201228

Keyword

nonn,easy

Author

Artur Jasinski, Nov 28 2011

Status

approved