This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A075869 5*n^2 - 9 is a square. 0
 3, 51, 915, 16419, 294627, 5286867, 94868979, 1702354755, 30547516611, 548152944243, 9836205479763, 176503545691491, 3167227616967075, 56833593559715859, 1019837456457918387, 18300240622682815107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Lim. n-> Inf. a(n)/a(n-1) = phi^6 = 9 + 4*Sqrt(5). 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 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 (18,-1). FORMULA a(n) = 3*sqrt(5)/10*((2+sqrt(5))^(2*n-1)-(2-sqrt(5))^(2*n-1)) = 18*a(n-1) - a(n-2) G.f.: 3x*(1-3x)/(1-18x+x^2). [From Philippe Deléham, Nov 17 2008] CROSSREFS Cf. 3*A007805. Sequence in context: A248341 A145242 A182512 * A126685 A246693 A187666 Adjacent sequences:  A075866 A075867 A075868 * A075870 A075871 A075872 KEYWORD nonn,easy AUTHOR Gregory V. Richardson, Oct 16 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.