The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A106257 Numbers k such that k^2 = 12*n^2 + 13. 1
 5, 11, 59, 149, 821, 2075, 11435, 28901, 159269, 402539, 2218331, 5606645, 30897365, 78090491, 430344779, 1087660229, 5993929541, 15149152715, 83484668795, 211000477781, 1162791433589, 2938857536219, 16195595401451 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Index entries for linear recurrences with constant coefficients, signature (0,14,0,-1). FORMULA k(1)=5, k(2)=11, k(3)=14*k(1)-k(2), k(4)=14*k(2)-k(1) then k(n)=14*k(n-2)-k(n-4). G.f.: -x*(x-1)*(5*x^2+16*x+5) / ((x^2-4*x+1)*(x^2+4*x+1)). - Corrected by Colin Barker, Apr 16 2014 a(2n) = (9*A001570(n)+A001570(n+1))/2, a(2n+1) = 5*A001570(n)-6*A007655(n). EXAMPLE 5^2=12*1^2+13 11^2=12*3^2+13 59^2=12*17^2+13 149^2=12*43^2+13 MATHEMATICA LinearRecurrence[{0, 14, 0, -1}, {5, 11, 59, 149}, 40] (* Harvey P. Dale, Oct 21 2021 *) PROG (PARI) Vec(-x*(x-1)*(5*x^2+16*x+5)/((x^2-4*x+1)*(x^2+4*x+1)) + O(x^100)) \\ Colin Barker, Apr 16 2014 CROSSREFS Cf. A106256. Sequence in context: A269454 A153209 A239026 * A104358 A104359 A104357 Adjacent sequences:  A106254 A106255 A106256 * A106258 A106259 A106260 KEYWORD nonn,easy AUTHOR Pierre CAMI, Apr 28 2005 EXTENSIONS Edited by Ralf Stephan, Jun 01 2007 STATUS approved

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

Last modified July 4 08:01 EDT 2022. Contains 355070 sequences. (Running on oeis4.)