This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A041683 Denominators of continued fraction convergents to sqrt(360). 2
 1, 1, 37, 38, 1405, 1443, 53353, 54796, 2026009, 2080805, 76934989, 79015794, 2921503573, 3000519367, 110940200785, 113940720152, 4212806126257, 4326746846409, 159975692596981, 164302439443390, 6074863512559021, 6239165952002411 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 36 and Q = -1; it is a strong divisibility sequence, that is, GCD(a(n),a(m)) = a(GCD(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Eric W. Weisstein, MathWorld: Lehmer Number Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1). FORMULA G.f.: -(x^2-x-1) / ((x^2-6*x-1)*(x^2+6*x-1)). - Colin Barker, Nov 21 2013 a(n) = 38*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 22 2013 From Peter Bala, May 28 2014: (Start) The following remarks assume an offset of 1. Let alpha = 3 + sqrt(10) and beta = 3 - sqrt(10) be the roots of the equation x^2 - 6*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even. a(n) = A005668(n+1) for n even; a(n) = 1/6*A005668(n+1) for n odd. a(n) = product {k = 1..floor((n-1)/2)} ( 36 + 4*cos^2(k*Pi/n) ). Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 36*a(2*n) + a(2*n - 1). (End) MATHEMATICA Denominator[Convergents[Sqrt, 30]] (* Vincenzo Librandi, Dec 22 2013 *) PROG (MAGMA) I:=[1, 1, 37, 38]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013 CROSSREFS Cf. A041682, A040341, A002530, A005668. Sequence in context: A071887 A168143 A111043 * A064172 A242989 A295801 Adjacent sequences:  A041680 A041681 A041682 * A041684 A041685 A041686 KEYWORD nonn,frac,easy AUTHOR EXTENSIONS More terms from Colin Barker, Nov 21 2013 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)