A145698 Numbers x such that (x+37)^3-x^3 is a square.

111, 76516, 45155207, 26641506492, 15718443685951, 9273855133215476, 5471558810153455767, 3228210424135405697932, 1904638678681079208334991, 1123733592211412597511957636

Offset

1,1

Links

Table of n, a(n) for n=1..10.

Index entries for linear recurrences with constant coefficients, signature (591,-591,1).

Formula

a(n+2)=590*a(n+1)-a(n)+10868.

a(n)=-(2717/147)+(9517/147)*{[295-28*sqrt(111)]^n+[295+28*sqrt(111)]^n}+(12779/2072)*sqrt(111)*{[295+28 *sqrt(111)]^n-[295-28*sqrt(111)]^n}. - Paolo P. Lava, Nov 25 2008

Example

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

Mathematica

CoefficientList[Series[(37 (-3-295 x+4 x^2))/(-1+591 x-591 x^2+x^3), {x, 0, 10}], x]  (* Harvey P. Dale, Feb 20 2011 *)

Prog

(PARI) Vec((111*x^2 - 65749*x + 76516)/(-x^3 + 591*x^2 - 591*x + 1)+O(x^99)) \\ Charles R Greathouse IV, May 28 2014

Crossrefs

Sequence in context: A015262 A201430 A262641 * A362920 A244845 A152775

Adjacent sequences: A145695 A145696 A145697 * A145699 A145700 A145701

Keyword

nonn,easy

Author

Richard Choulet, Oct 16 2008

Status

approved