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 A075839 11*n^2 - 2 is a square. 11
 1, 19, 379, 7561, 150841, 3009259, 60034339, 1197677521, 23893516081, 476672644099, 9509559365899, 189714514673881, 3784780734111721, 75505900167560539, 1506333222617099059, 30051158552174420641, 599516837820871313761, 11960285597865251854579 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Lim. n -> inf. a(n)/a(n-1) = 10 + 3*sqrt(11). Positive values of x (or y) satisfying x^2 - 20xy + y^2 + 18 = 0. - Colin Barker, Feb 18 2014 REFERENCES A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248-268, 1966. L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, pp. 341-400. Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, pp. 139-147. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Tanya Khovanova, Recursive Sequences J. J. O'Connor and E. F. Robertson, Pell's Equation Eric Weisstein's World of Mathematics, Pell Equation. Index entries for linear recurrences with constant coefficients, signature (20,-1). FORMULA 11*a(n)^2-9*A083043(n)^2=2. a(n) = ((3+sqrt(11))*(10+3*sqrt(11))^n - (3-sqrt(11))*(10-3*sqrt(11))^n)/(2*sqrt(11)). - Dean Hickerson, Dec 09 2002 G.f.: (1-x)/(1-20*x+x^2). a(n)=20*a(n-1)-a(n-2), n>1. - Michael Somos, Oct 29 2002 Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)) then a(n)=q(n, 18). - Benoit Cloitre, Dec 06 2002 a(-1-n)=a(n). - Michael Somos, Apr 18 2003 MATHEMATICA LinearRecurrence[{20, -1}, {1, 19}, 20] (* Harvey P. Dale, Apr 13 2012 *) CoefficientList[Series[(1 - x)/(1 - 20 x + x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Feb 20 2014 *) a[c_, n_] := Module[{},    p := Length[ContinuedFraction[ Sqrt[ c]][[2]]];    d := Denominator[Convergents[Sqrt[c], n p]];    t := Table[d[[1 + i]], {i, 0, Length[d] - 1, p}];    Return[t]; ] (* Complement of A041015 *) a[11, 20] (* Gerry Martens, Jun 07 2015 *) PROG (PARI) a(n)=subst(poltchebi(n+1)+poltchebi(n), x, 10)/11 (MAGMA) I:=[1, 19]; [n le 2 select I[n] else 20*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 20 2014 CROSSREFS Row 20 of array A094954. Cf. A075844, A221762, A041015. Cf. similar sequences listed in A238379. Sequence in context: A041686 A263371 A023283 * A158592 A072359 A222835 Adjacent sequences:  A075836 A075837 A075838 * A075840 A075841 A075842 KEYWORD easy,nonn AUTHOR Gregory V. Richardson, Oct 14 2002 EXTENSIONS More terms from Colin Barker, Feb 18 2014 STATUS approved

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Last modified June 20 11:38 EDT 2019. Contains 324234 sequences. (Running on oeis4.)