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A199405 y-values in the solution to 13*x^2 - 12 = y^2. 2
1, 14, 25, 155, 274, 1691, 2989, 18446, 32605, 201215, 355666, 2194919, 3879721, 23942894, 42321265, 261176915, 461654194, 2849003171, 5035874869, 31077857966, 54932969365, 339007434455, 599226788146, 3698003921039, 6536561700241, 40339035696974 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

When are both n+1 and 13*n+1 perfect squares? This problem gives the equation 13*x^2-12=y^2.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,11,0,-1).

FORMULA

a(n+4) = 11*a(n+2)-a(n) with a(1)=1, a(2)=14, a(3)=25, a(4)=155.

G.f.: x*(1+x)*(1+13*x+x^2)/((1+3*x-x^2)*(1-3*x-x^2)). - Bruno Berselli, Nov 08 2011

a(n) = 2^(-1-n)*(2*(3-sqrt(13))^n+(-3-sqrt(13))^n*(-3+sqrt(13))-3*(-3+sqrt(13))^n-sqrt(13)*(-3+sqrt(13))^n+2*(3+sqrt(13))^n). - Colin Barker, Mar 27 2016

MATHEMATICA

LinearRecurrence[{0, 11, 0, -1}, {1, 14, 25, 155}, 50]  (* Bruno Berselli, Nov 08 2011 *)

PROG

(MAGMA) m:=27; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x)*(1+13*x+x^2)/((1+3*x-x^2)*(1-3*x-x^2)))); // Bruno Berselli, Nov 08 2011

(PARI) Vec(x*(1+x)*(1+13*x+x^2)/((1+3*x-x^2)*(1-3*x-x^2)) + O(x^50)) \\ Colin Barker, Mar 27 2016

CROSSREFS

Cf. A199404.

Sequence in context: A174519 A079505 A039604 * A256573 A030786 A094163

Adjacent sequences:  A199402 A199403 A199404 * A199406 A199407 A199408

KEYWORD

nonn,easy

AUTHOR

Sture Sjöstedt, Nov 05 2011

EXTENSIONS

More terms from Bruno Berselli, Nov 08 2011

STATUS

approved

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Last modified June 16 14:16 EDT 2021. Contains 345057 sequences. (Running on oeis4.)