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 A114052 x such that x^2 - 27*y^2 = 1. 1
 1, 26, 1351, 70226, 3650401, 189750626, 9863382151, 512706121226, 26650854921601, 1385331749802026, 72010600134783751, 3743165875258953026, 194572614913330773601, 10114032809617941274226, 525735133485219615486151 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A Pellian equation (Pell's equation). - Benoit Cloitre, Feb 03 2006 LINKS Robert Israel, Table of n, a(n) for n = 0..524 Tanya Khovanova, Recursive Sequences John Robertson, Home page. Index entries for linear recurrences with constant coefficients, signature (52,-1). FORMULA a(0) = 1, a(1) = 26 then a(n) = 52*a(n-1) - a(n-2). - Benoit Cloitre, Feb 03 2006 G.f.: (1 - 26x)/(1 - 52x + x^2). - Philippe Deléham, Nov 18 2008 a(n) = 1/2*(1+(26+15*sqrt(3))^(2*n))/(26+15*sqrt(3))^n. - Gerry Martens, May 30 2015 MAPLE f:= gfun:-rectoproc({a(n)=52*a(n-1)-a(n-2), a(0)=1, a(1)=26}, a(n), remember): map(f, [\$0..40]); # Robert Israel, Jun 01 2015 MATHEMATICA A114052[n_] := 1/2(1 + (26 + 15 Sqrt[3])^(2 n))/(26 + 15 Sqrt[3])^n; Table[A114052[n] // FullSimplify, {n, 0, 20}] (* Gerry Martens, May 30 2015 *) CoefficientList[Series[(1 - 26 x)/(1 - 52 x + x^2), {x, 0, 33}], x] (* Vincenzo Librandi, May 31 2015 *) LinearRecurrence[{52, -1}, {1, 26}, 20] (* Harvey P. Dale, Jul 30 2017 *) PROG (PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", "))) (PARI) a0=1; a1=26; for(n=2, 30, a2=52*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) \\ Benoit Cloitre, Feb 03 2006 (MAGMA)  I:=[1, 26]; [n le 2 select I[n] else 52*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, May 31 2015 CROSSREFS Sequence in context: A160311 A220955 A106710 * A042303 A042300 A282884 Adjacent sequences:  A114049 A114050 A114051 * A114053 A114054 A114055 KEYWORD easy,nonn AUTHOR Cino Hilliard, Feb 01 2006 EXTENSIONS More terms from Benoit Cloitre, Feb 03 2006 More terms from Robert G. Wilson v, Mar 17 2006 STATUS approved

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Last modified July 22 19:35 EDT 2018. Contains 312918 sequences. (Running on oeis4.)