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!)
 A041061 Denominators of continued fraction convergents to sqrt(37). 12
 1, 12, 145, 1752, 21169, 255780, 3090529, 37342128, 451196065, 5451694908, 65871534961, 795910114440, 9616792908241, 116197425013332, 1403985893068225, 16964028141832032, 204972323595052609, 2476631911282463340, 29924555258984612689, 361571295019097815608 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sqrt(37) = 6.08276253... = 12/2 + 12/145 + 12/(145*21169) + 12/(21169*3090529) + ... - Gary W. Adamson, Jun 13 2008 For positive n, a(n) equals the permanent of the n X n tridiagonal matrix with 12's along the main diagonal and 1's along the superdiagonal and the subdiagonal. [From John M. Campbell, Jul 08 2011] a(n) equals the number of words of length n on alphabet {0,1,...,12} avoiding runs of zeros of odd lengths. - Milan Janjic, Jan 28 2015 LINKS Nathaniel Johnston, Table of n, a(n) for n = 0..500 Tanya Khovanova, Recursive Sequences Pablo Lam-Estrada, Myriam Rosalía Maldonado-Ramírez, José Luis López-Bonilla, Fausto Jarquín-Zárate, The sequences of Fibonacci and Lucas for each real quadratic fields Q(Sqrt(d)), arXiv:1904.13002 [math.NT], 2019. Index entries for linear recurrences with constant coefficients, signature (12,1). FORMULA a(n) = F(n, 12), the n-th Fibonacci polynomial evaluated at x=12. - T. D. Noe, Jan 19 2006 a(n) = 12*a(n-1)+a(n-2), n>1 ; a(0)=1, a(1)=12. G.f.: 1/(1-12*x-x^2). [Philippe Deléham, Nov 21 2008] a(n) = ((6+sqrt(37))^(n+1)-(6-sqrt(37))^(n+1))/(2*sqrt(37)). [Rolf Pleisch, May 14 2011] MATHEMATICA a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*12, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *) Denominator[Convergents[Sqrt[37], 30]] (* or *) LinearRecurrence[{12, 1}, {1, 12}, 30] (* Harvey P. Dale, May 26 2014 *) PROG (Sage) [lucas_number1(n, 12, -1) for n in range(1, 18)] /* Zerinvary Lajos, Apr 28 2009 */ CROSSREFS Cf. A010491, A041060. Cf. A243399. Sequence in context: A075619 A055332 A288792 * A174227 A041266 A015501 Adjacent sequences:  A041058 A041059 A041060 * A041062 A041063 A041064 KEYWORD nonn,frac,easy,changed AUTHOR 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 7 14:24 EST 2019. Contains 329845 sequences. (Running on oeis4.)