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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

Table of n, a(n) for n=1..13.

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 A167448

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 December 3 04:39 EST 2016. Contains 278698 sequences.