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A199336 x-values in the solution to 15*x^2 - 14 = y^2. 5
1, 3, 5, 23, 39, 181, 307, 1425, 2417, 11219, 19029, 88327, 149815, 695397, 1179491, 5474849, 9286113, 43103395, 73109413, 339352311, 575589191, 2671715093, 4531604115, 21034368433, 35677243729, 165603232371, 280886345717, 1303791490535, 2211413522007 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

When are both n+1 and 15*n+1 perfect squares? This problem gives the equation 15*x^2-14=y^2.

Values of x (or y) in the solutions to x^2 - 8xy + y^2 + 14 = 0. - Colin Barker, Feb 05 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..250

Index entries for linear recurrences with constant coefficients, signature (0, 8, 0, -1).

FORMULA

a(n+4) = 8*a(n+2) - a(n), a(1)=1, a(2)=3 ,a(3)=5, a(4)=23.

G.f.: x*(1-x)*(1+4*x+x^2)/(1-8*x^2+x^4). - Bruno Berselli, Nov 08 2011

MATHEMATICA

LinearRecurrence[{0, 8, 0, -1}, {1, 3, 5, 23}, 50] (* T. D. Noe, Nov 07 2011 *)

PROG

(Magma) m:=29; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)*(1+4*x+x^2)/(1-8*x^2+x^4))); // Bruno Berselli, Nov 08 2011

CROSSREFS

Cf. A198947, A199338.

Essentially the second differences of A237262. Cf. also A322780.

Sequence in context: A296927 A215132 A091157 * A214876 A280273 A036952

Adjacent sequences: A199333 A199334 A199335 * A199337 A199338 A199339

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 28 17:08 EST 2023. Contains 359895 sequences. (Running on oeis4.)