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A145121 Numbers n such that there exists x in N : (x+19)^3-x^3=n^2. 1
361, 108661, 32815261, 9910100161, 2992817433361, 903820954774861, 272950935524574661, 82430278707466772761, 24893671218719440799161, 7517806277774563654573861, 2270352602216699504240506861, 685638968063165475716978498161, 207060698002473756967023265937761 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (302,-1).

FORMULA

a(n+2) = 302*a(n+1)-a(n).

a(n) = (361/2)*{[151+20*sqrt(57)]^n+[151-20*sqrt(57)]^n}-(95/4)*sqrt(57)*{[151-20 *sqrt(57)]^n-[151+20*sqrt(57)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

a(n) = 361*A145123(n). - Colin Barker, Oct 19 2014

G.f.: -361*x*(x-1) / (x^2-302*x+1). - Colin Barker, Oct 19 2014

EXAMPLE

a(1)=361 because 57^3-38^3=361^2.

MATHEMATICA

CoefficientList[Series[361 (1 - x)/(x^2 - 302 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 19 2014

PROG

(PARI) Vec(-361*x*(x-1)/(x^2-302*x+1) + O(x^20)) \\ Colin Barker, Oct 19 2014

(MAGMA) I:=[361, 108661]; [n le 2 select I[n] else 302*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 19 2014

CROSSREFS

Sequence in context: A302957 A232081 A231770 * A062788 A048289 A191216

Adjacent sequences:  A145118 A145119 A145120 * A145122 A145123 A145124

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 02 2008

EXTENSIONS

Editing and more terms from Colin Barker, Oct 19 2014

STATUS

approved

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Last modified April 19 16:58 EDT 2019. Contains 322283 sequences. (Running on oeis4.)