This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A162563 a(n) = ((5+sqrt(3))*(2+sqrt(3))^n + (5-sqrt(3))*(2-sqrt(3))^n)/2. 3
 5, 13, 47, 175, 653, 2437, 9095, 33943, 126677, 472765, 1764383, 6584767, 24574685, 91713973, 342281207, 1277410855, 4767362213, 17792037997, 66400789775, 247811121103, 924843694637, 3451563657445, 12881410935143, 48074080083127 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Binomial transform of A162562. Second binomial transform of A162813. Inverse binomial transform of A162814. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-1). FORMULA a(n) = 4*a(n-1) - a(n-2) for n > 1; a(0) = 5, a(1) = 13. G.f.: (5-7*x)/(1-4*x+x^2). a(n) = 4*a(n-1) - a(n-2), with a(0)=5 and a(1)=13. - Paolo P. Lava, Jul 15 2009 MATHEMATICA LinearRecurrence[{4, -1}, {5, 13}, 30] (* Harvey P. Dale, Aug 25 2014 *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((5+r)*(2+r)^n+(5-r)*(2-r)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009 CROSSREFS Cf. A162562, A162813, A162814. Sequence in context: A152925 A304964 A120790 * A250133 A025545 A146152 Adjacent sequences:  A162560 A162561 A162562 * A162564 A162565 A162566 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Jul 18 2009 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 July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)