This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A094347 a(n) = 14*a(n-1)-a(n-2); a(0) = a(1) = 2. 6
 2, 2, 26, 362, 5042, 70226, 978122, 13623482, 189750626, 2642885282, 36810643322, 512706121226, 7141075053842, 99462344632562, 1385331749802026, 19295182152595802, 268747218386539202, 3743165875258953026 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Even x satisfying the Pellian x^2 - 3*y^2 = 1. For corresponding y see A028230. LINKS R. K. Guy, Letter to N. J. A. Sloane concerning A001075, A011943, A094347 [Scanned and annotated letter, included with permission] Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (14,-1). FORMULA G.f.: 2*(1-13x)/(1-14*x+x^2). [Philippe Deléham, Nov 17 2008] a(n) = ( (2+sqrt(3))^(2*n-1) + (2-sqrt(3))^(2*n-1) )/2. - Gerry Martens, Jun 03 2015 a(n) = (1/2)*sqrt(4+(-2*sqrt(-2+(7-4*sqrt(3))^(2*n)+(7+4*sqrt(3))^(2*n))+sqrt(3)*sqrt(2+(7-4*sqrt(3))^(2*n)+(7+4*sqrt(3))^(2*n)))^2). - Gerry Martens, Jun 03 2015 MATHEMATICA LinearRecurrence[{14, -1}, {2, 2}, 40] (* or *) CoefficientList[ Series[2(1-13x)/(1-14x+x^2), {x, 0, 39}], x] (* Harvey P. Dale, Apr 23 2011 *) CROSSREFS a(n) = 2*A001570(n). Bisection of A001075. Cf. A028230. Sequence in context: A195967 A120979 A032000 * A236286 A288208 A024577 Adjacent sequences:  A094344 A094345 A094346 * A094348 A094349 A094350 KEYWORD nonn,easy AUTHOR Lekraj Beedassy, Jun 03 2004 EXTENSIONS Corrected by Lekraj Beedassy, Jun 11 2004 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.