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A145718 Numbers x such that there exists n in N with (x+127)^3-x^3=n^2. 2
762, 1676527, 3403477826, 6909058439031, 14025385227883882, 28471525103545970207, 57797181934813091765106, 117328250856145472737323751, 238176291440793374843675578202, 483497754296559694787188686555087, 981500203045724739624618190031377186 (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 (2031,-2031,1).

FORMULA

a(n+2) = 2030*a(n+1)-a(n)+128778.

a(n) = -(127/2)+(1651/4)*{[1015+52*sqrt(381)]^n+[1015-52*sqrt(381)]^n}+(127/6)*sqrt(381)*{[1015+52*sqrt(381)]^n-[1015-52*sqrt(381)]^n} with n>=0. -Paolo P. Lava, Nov 25 2008

a(n) = 127*A145720(n). - Colin Barker, Oct 18 2014

G.f.: 127*x*(7*x^2-1015*x-6) / ((x-1)*(x^2-2030*x+1)). - Colin Barker, Oct 18 2014

EXAMPLE

a(1)=762 because the first relation is (762+127)^3-762^3=16129^2.

MATHEMATICA

CoefficientList[Series[127 (7 x^2 - 1015 x - 6)/((x - 1) (x^2 - 2030 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 18 2014 *)

PROG

(PARI) Vec(127*x*(7*x^2-1015*x-6)/((x-1)*(x^2-2030*x+1)) + O(x^20)) \\ Colin Barker, Oct 18 2014

(MAGMA) I:=[762, 1676527]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2)+128778: n in [1..20]]; // Vincenzo Librandi, Oct 18 2014

CROSSREFS

Cf. A145720.

Sequence in context: A326369 A210081 A083645 * A049516 A049517 A121321

Adjacent sequences:  A145715 A145716 A145717 * A145719 A145720 A145721

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 16 2008

EXTENSIONS

Editing and more terms from Colin Barker, Oct 18 2014

STATUS

approved

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Last modified March 2 09:45 EST 2021. Contains 341746 sequences. (Running on oeis4.)