login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)