A199404 x-values in the solution to 13*x^2 - 12 = y^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

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