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A145334 Numbers x such that (x+43)^3-x^3 is a square. 1
1118, 38413663, 1294925303334, 43651931937700199, 1471506624324949129678, 49604488262342103224469903, 1672167297852045675371932025174, 56368759560987971454445725344870359, 1900190883128737219877319726003648501438 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (33711,-33711,1).

FORMULA

a(n+2) = 33710*a(n+1)-a(n)+724722.

a(n) = -(43/2)+(2279/4)*{[16855+1484*sqrt(129)]^n+[16855-1484*sqrt(129)]^n}-(301/6)*sqrt(129)*{[16855-1484*sqrt(129)]^n -[16855+1484*sqrt(129)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: 43*x*(27*x^2-16855*x-26) / ((x-1)*(x^2-33710*x+1)). - Colin Barker, Oct 21 2014

EXAMPLE

a(1)=1118 because the first relation is : (1118+43)^3-1118^3=12943^2.

MATHEMATICA

CoefficientList[Series[43 (27 x^2 - 16855 x - 26)/((x - 1) (x^2 - 33710 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

LinearRecurrence[{33711, -33711, 1}, {1118, 38413663, 1294925303334}, 20] (* Harvey P. Dale, Feb 22 2017 *)

PROG

(PARI) Vec(43*x*(27*x^2-16855*x-26)/((x-1)*(x^2-33710*x+1)) + O(x^20)) \\ Colin Barker, Oct 21 2014

(MAGMA) I:=[1118, 38413663, 1294925303334]; [n le 3 select I[n] else 33711*Self(n-1)-33711*Self(n-2)+Self(n-3): n in [1..10]]; // Vincenzo Librandi, Oct 21 2014

CROSSREFS

Sequence in context: A251360 A201034 A264312 * A134211 A171004 A235275

Adjacent sequences:  A145331 A145332 A145333 * A145335 A145336 A145337

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 08 2008

EXTENSIONS

Editing from Colin Barker, Oct 21 2014

STATUS

approved

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Last modified December 5 03:52 EST 2021. Contains 349530 sequences. (Running on oeis4.)