

A145124


Numbers x such that there exists n in N : (x+1)^3x^3=19*n^2.


2



2, 757, 228762, 69085517, 20863597522, 6300737366277, 1902801821018282, 574639849210155037, 173539331659645803042, 52408303521363822363797, 15827134124120214708063802, 4779742097180783478012904557, 1443466286214472490145189112562
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..13.
Index to sequences with 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+[15120*sqrt(57)]^n}(1/6)*sqrt(57)*{[15120 *sqrt(57)]^n[151+20*sqrt(57)]^n} with n>=0.  Paolo P. Lava, Nov 25 2008
G.f.: x*(2151*x+3*x^2) / ( (x1)*(x^2302*x+1) ).  R. J. Mathar, Nov 27 2011


EXAMPLE

a(1)=2 because 3^32^3=19*1.


PROG

(PARI) Vec(x*(2151*x+3*x^2)/((x1)*(x^2302*x+1)) + O(x^30)) \\ Colin Barker, Oct 18 2014


CROSSREFS

Cf. A145123.
Sequence in context: A109949 A151591 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



