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A133275 Numbers X such that 30*X^2-45 is a square. 2
3, 63, 1383, 30363, 666603, 14634903, 321301263, 7053992883, 154866542163, 3400009934703, 74645352021303, 1638797734533963, 35978904807725883, 789897108035435463, 17341757471971854303, 380728767275345359203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Positive values of x (or y) satisfying x^2 - 22xy + y^2 + 180 = 0. - Colin Barker, Feb 19 2014

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (22,-1).

FORMULA

a(n+2) = 22*a(n+1)-a(n).

a(n+1) = 11*a(n)+2*(30*a(n)^2-45)^0.5.

G.f.: -3*x*(-1+x)/(1-22*x+x^2). - R. J. Mathar, Nov 14 2007

a(n) = (3/2)*(11+2*sqrt(30))^n+(1/4)*(11+2*sqrt(30))^n*sqrt(30)+(3/2)*(11-2*sqrt(30))^n-(1/4) *sqrt(30)*(11-2*sqrt(30))^n for n>=0. [Paolo P. Lava, Aug 06 2008]

a(n) = 3*A157014(n). - Colin Barker, Feb 19 2014

MATHEMATICA

CoefficientList[Series[3 (1 - x)/(1 - 22 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 21 2014 *)

PROG

(MAGMA) I:=[3, 63]; [n le 2 select I[n] else 22*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 21 2014

CROSSREFS

Cf. A157014.

Sequence in context: A151993 A120053 A139293 * A258657 A123687 A159605

Adjacent sequences:  A133272 A133273 A133274 * A133276 A133277 A133278

KEYWORD

nonn,easy

AUTHOR

Richard Choulet, Oct 16 2007

EXTENSIONS

More terms from Paolo P. Lava, Aug 06 2008

STATUS

approved

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Last modified January 16 15:31 EST 2019. Contains 319195 sequences. (Running on oeis4.)