This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A097729 Pell equation solutions (6*a(n))^2 - 37*b(n)^2 = -1 with b(n):=A097730(n), n>=0. 4
 1, 147, 21461, 3133159, 457419753, 66780150779, 9749444593981, 1423352130570447, 207799661618691281, 30337327244198356579, 4429041977991341369253, 646609791459491641554359, 94400600511107788325567161, 13781841064830277603891251147, 2012054394864709422379797100301 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..461 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (146,-1). FORMULA G.f.: (1 + x)/(1 - 2*73*x + x^2). a(n) = S(n, 2*73) + S(n-1, 2*73) = S(2*n, 2*sqrt(37)), with Chebyshev polynomials of the second kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x). a(n) = ((-1)^n)*T(2*n+1, 6*I)/(6*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120. a(n) = 146*a(n-1)-a(n-2), n>1; a(0)=1, a(1)=147. - Philippe Deléham, Nov 18 2008 a(n) = (1/6)*sinh((2*n + 1)*arcsinh(6)). - Bruno Berselli, Apr 03 2018 EXAMPLE (x,y) = (6,1), (882,145), (128766,21169), ... give the positive integer solutions to x^2 - 37*y^2 =-1. MATHEMATICA LinearRecurrence[{146, -1}, {1, 147}, 20] (* Harvey P. Dale, Sep 24 2012 *) PROG (PARI) x='x+O('x^99); Vec((1+x)/(1-2*73*x+x^2)) \\ Altug Alkan, Apr 05 2018 CROSSREFS Cf. A097728 for S(n, 2*73). Cf. similar sequences of the type (1/k)*sinh((2*n+1)*arcsinh(k)) listed in A097775. Sequence in context: A183741 A020328 A075925 * A214139 A215656 A214619 Adjacent sequences:  A097726 A097727 A097728 * A097730 A097731 A097732 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 EXTENSIONS Two more terms {a(12) & a(13)) from Harvey P. Dale, Sep 24 2012 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.

Last modified August 15 09:12 EDT 2018. Contains 313756 sequences. (Running on oeis4.)