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A145321
Numbers x such that (x+31)^3-x^3 is a square.
1
682, 16951327, 411951524722, 10011245937219367, 243293298354353908762, 5912513726596262753891407, 143685908340449079090715440802, 3491854938577079793466303888855447, 84859058573614284800369038016250008842
OFFSET
1,1
FORMULA
a(n+2) = 24302*a(n+1)-a(n)+376650.
G.f.: 31*x*(23*x^2-12151*x-22) / ((x-1)*(x^2-24302*x+1)). - Colin Barker, Oct 21 2014
EXAMPLE
a(1)=682 because the first relation is : (682+31)^3-682^3=6727^2.
MATHEMATICA
CoefficientList[Series[31(23 x^2 - 12151 x - 22)/((x - 1) (x^2 - 24302 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)
PROG
(PARI) Vec(31*x*(23*x^2-12151*x-22)/((x-1)*(x^2-24302*x+1)) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[682, 16951327, 411951524722]; [n le 3 select I[n] else 24303*Self(n-1)-24303*Self(n-2)+Self(n-3): n in [1..10]]; // Vincenzo Librandi, Oct 21 2014
CROSSREFS
Sequence in context: A200860 A184547 A327417 * A175155 A174105 A320772
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Oct 07 2008
EXTENSIONS
Editing from Colin Barker, Oct 21 2014
STATUS
approved