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A199404 x-values in the solution to 13*x^2 - 12 = y^2. 2
1, 4, 7, 43, 76, 469, 829, 5116, 9043, 55807, 98644, 608761, 1076041, 6640564, 11737807, 72437443, 128039836, 790171309, 1396700389, 8619446956, 15235664443, 94023745207, 166195608484, 1025641750321, 1812916028881, 11188035508324, 19775880709207 (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..250

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)=4, a(3)=7, a(4)=43.

G.f.: x*(1-x)*(1+5*x+x^2)/(1-11*x^2+x^4). - Bruno Berselli, Nov 08 2011

MATHEMATICA

LinearRecurrence[{0, 11, 0, -1}, {1, 4, 7, 43}, 50] (* T. D. Noe, Nov 07 2011 *)

PROG

(MAGMA) m:=28; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-x)*(1+5*x+x^2)/(1-11*x^2+x^4))); // Bruno Berselli, Nov 08 2011

CROSSREFS

Cf. A199405.

Sequence in context: A152450 A059213 A093102 * A284971 A139030 A115439

Adjacent sequences:  A199401 A199402 A199403 * A199405 A199406 A199407

KEYWORD

nonn,easy

AUTHOR

Sture Sjöstedt, Nov 05 2011

EXTENSIONS

More terms from T. D. Noe, Nov 07 2011

STATUS

approved

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Last modified January 17 16:33 EST 2018. Contains 297822 sequences.