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 A145124 Numbers x such that there exists n in N : (x+1)^3-x^3=19*n^2. 3
 2, 757, 228762, 69085517, 20863597522, 6300737366277, 1902801821018282, 574639849210155037, 173539331659645803042, 52408303521363822363797, 15827134124120214708063802, 4779742097180783478012904557, 1443466286214472490145189112562 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Index entries for linear recurrences with constant coefficients, signature (303,-303,1). FORMULA a(n+2) = 302*a(n+1)-a(n)+150. a(n) = -(1/2)+(5/4)*{[151+20*sqrt(57)]^n+[151-20*sqrt(57)]^n}-(1/6)*sqrt(57)*{[151-20 *sqrt(57)]^n-[151+20*sqrt(57)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008 G.f.: x*(-2-151*x+3*x^2) / ( (x-1)*(x^2-302*x+1) ). - R. J. Mathar, Nov 27 2011 EXAMPLE a(1)=2 because 3^3-2^3=19*1. PROG (PARI) Vec(x*(-2-151*x+3*x^2)/((x-1)*(x^2-302*x+1)) + O(x^30)) \\ Colin Barker, Oct 18 2014 CROSSREFS Cf. A145123. Sequence in context: A151591 A252986 A247080 * A102969 A179960 A344663 Adjacent sequences:  A145121 A145122 A145123 * A145125 A145126 A145127 KEYWORD easy,nonn AUTHOR Richard Choulet, Oct 02 2008 EXTENSIONS Editing and more terms from Colin Barker, Oct 18 2014 STATUS approved

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Last modified September 22 03:20 EDT 2021. Contains 347605 sequences. (Running on oeis4.)