A145697 Numbers n such that there exists x in N with (x+37)^3-x^3=n^2.

1369, 806341, 475739821, 280685688049, 165604080209089, 97706126637674461, 57646449112147722901, 34011307270040518837129, 20066613642874793966183209, 11839268037988858399529256181, 6985148075799783580928294963581, 4121225525453834323889294499256609

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..360

Index entries for linear recurrences with constant coefficients, signature (590,-1).

Formula

a(n+2) = 590*a(n+1)-a(n).

a(n) = (1369/2)*{[295-28*sqrt(111)]^n+[295+28*sqrt(111)]^n}+(259/4)*sqrt(111)*{[295+28*sqrt(111)]^n-[295-28 *sqrt(111)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: -1369*x*(x-1) / (x^2-590*x+1). - Colin Barker, Oct 18 2014

Example

a(1)=1369 because the first relation is (111+37)^3-111^3=1369^2.

Mathematica

LinearRecurrence[{590, -1}, {1369, 806341}, 20] (* Harvey P. Dale, Apr 10 2014 *)
CoefficientList[Series[1369 (1 - x)/(x^2 - 590 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 18 2014 *)

Prog

(PARI) Vec(-1369*x*(x-1)/(x^2-590*x+1) + O(x^20)) \\ Colin Barker, Oct 18 2014
(Magma) I:=[1369, 806341]; [n le 2 select I[n] else 590*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Oct 18 2014

Crossrefs

Sequence in context: A331464 A167724 A156574 * A045107 A031752 A031662

Adjacent sequences: A145694 A145695 A145696 * A145698 A145699 A145700

Keyword

easy,nonn

Author

Richard Choulet, Oct 16 2008

Extensions

Edited by Colin Barker, Oct 18 2014

Status

approved