This site is supported by donations to The OEIS Foundation.

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086928 a(n) = 12a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 12, a(n) = (6+sqrt(37))^n + (6-sqrt(37))^n. 2
 2, 12, 146, 1764, 21314, 257532, 3111698, 37597908, 454286594, 5489037036, 66322731026, 801361809348, 9682664443202, 116993335127772, 1413602685976466, 17080225566845364, 206376309488120834 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n+1)/a(n) converges to (6+sqrt(37)) =12.0827625... a(0)/a(1)=2/12; a(1)/a(2)=12/146; a(2)/a(3)=146/1764; a(3)/a(4)=1764/21314; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.0827625... = 1/(6+sqrt(37)) = (sqrt(37)-6). LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (12,1). FORMULA G.f.: (2-12*x)/(1-12*x-x^2). [From Philippe Deléham, Nov 21 2008] EXAMPLE a(4) = 21314 = 12a(3) + a(2) = 12*1764 + 146 = (6+sqrt(37))^4 + (6-sqrt(37))^4 = 21313.999953 + 0.000047 = 21314 MATHEMATICA LinearRecurrence[{12, 1}, {2, 12}, 20] (* Harvey P. Dale, Oct 31 2016 *) CROSSREFS Cf. A001927. Sequence in context: A010790 A221101 A187748 * A228551 A001927 A105558 Adjacent sequences:  A086925 A086926 A086927 * A086929 A086930 A086931 KEYWORD easy,nonn AUTHOR Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 21 2003 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.