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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
OFFSET
1,1
FORMULA
a(n+2) = 2030*a(n+1)-a(n)+128778.
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
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Oct 16 2008
EXTENSIONS
Editing and more terms from Colin Barker, Oct 18 2014
STATUS
approved