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A145720 Numbers x such that there exists n in N with (x+1)^3-x^3=127*n^2. 3
6, 13201, 26799038, 54402034953, 110436104156566, 224185237035795041, 455095920746559777678, 923844494930279312892313, 1875403869612546258611618726, 3807068931468973974702273122481, 7728348055478147556099355827018718, 15688542745551708069907717626574876073 (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)+1014.

a(n) = -(1/2)+(13/4)*{[1015+52*sqrt(381)]^n+[1015-52*sqrt(381)])^n}+(1/6)*sqrt(381)*{[1015+52*sqrt(381)]^n-[1015-52*sqrt(381)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

a(n) = A145718(n)/127. - Colin Barker, Oct 18 2014

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

EXAMPLE

a(1)=6 because the first relation is 7^3-6^3=127*1^2.

MATHEMATICA

CoefficientList[Series[(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(x*(7*x^2-1015*x-6)/((x-1)*(x^2-2030*x+1)) + O(x^20)) \\ Colin Barker, Oct 18 2014

(MAGMA) I:=[6, 13201]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2)+1014: n in [1..20]]; // Vincenzo Librandi, Oct 18 2014

CROSSREFS

Cf. A145718.

Sequence in context: A146202 A227889 A242676 * A093897 A062782 A036773

Adjacent sequences:  A145717 A145718 A145719 * A145721 A145722 A145723

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 January 28 10:02 EST 2020. Contains 331319 sequences. (Running on oeis4.)