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 A075844 Numbers n such that 11*n^2 + 4 is a square. 3
 0, 6, 120, 2394, 47760, 952806, 19008360, 379214394, 7565279520, 150926376006, 3010962240600, 60068318435994, 1198355406479280, 23907039811149606, 476942440816512840, 9514941776519107194, 189821893089565631040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Lim. n-> Inf. a(n)/a(n-1) = 10 + 3*sqrt(11). 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 Harvey P. Dale, Table of n, a(n) for n = 0..750 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 a(n) = ((10+3*sqrt(11))^n - (10-3*sqrt(11))^n) / sqrt(11). a(n) = 20*a(n-1) - a(n-2). G.f.: 6*x/(1 - 20*x + x^2). a(n) = (1/3)*(A075839(n+1) - A075839(n)), n>=1. - N. J. A. Sloane, Sep 22 2004 a(n) = 6*A075843(n). - R. J. Mathar, Jul 03 2011 MAPLE seq(coeff(series(6*x/(1-20*x+x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Dec 06 2019 MATHEMATICA LinearRecurrence[{20, -1}, {0, 6}, 20] (* Harvey P. Dale, May 28 2012 *) PROG (PARI) my(x='x+O('x^20)); concat([0], Vec(6*x/(1-20*x+x^2))) \\ G. C. Greubel, Dec 06 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 20); [0] cat Coefficients(R!( 6*x/(1 - 20*x + x^2) )); // G. C. Greubel, Dec 06 2019 (Sage) def A075844_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( 6*x/(1-20*x+x^2) ).list() A075844_list(20) # G. C. Greubel, Dec 06 2019 (GAP) a:=[0, 6];; for n in [3..20] do a[n]:=20*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 06 2019 CROSSREFS Cf. A221762. Sequence in context: A246191 A246611 A185757 * A029697 A248045 A280627 Adjacent sequences:  A075841 A075842 A075843 * A075845 A075846 A075847 KEYWORD nonn,easy,changed AUTHOR Gregory V. Richardson, Oct 14 2002 STATUS approved

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Last modified December 10 15:09 EST 2019. Contains 329896 sequences. (Running on oeis4.)