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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A164602 a(n) = ((1+4*sqrt(2))*(1+2*sqrt(2))^n + (1-4*sqrt(2))*(1-2*sqrt(2))^n)/2. 3
 1, 17, 41, 201, 689, 2785, 10393, 40281, 153313, 588593, 2250377, 8620905, 32994449, 126335233, 483631609, 1851609849, 7088640961, 27138550865, 103897588457, 397765032969, 1522813185137, 5829981601057, 22319655498073 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A164703. Inverse binomial transform of A164603. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..177 from Vincenzo Librandi) Index entries for linear recurrences with constant coefficients, signature (2,7). FORMULA a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 17. G.f.: (1+15*x)/(1-2*x-7*x^2). E.g.f.: exp(x)*(cosh(2*sqrt(2)*x) + 4*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 11 2017 MATHEMATICA Simplify/@Table[1/2((1-4Sqrt[2])(1-2Sqrt[2])^n+(1+2Sqrt[2])^n(1+4 Sqrt[2])), {n, 0, 25}] (* Harvey P. Dale, Jul 26 2011 *) PROG (Magma) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((1+4*r)*(1+2*r)^n+(1-4*r)*(1-2*r)^n)/2: n in [0..22] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 23 2009 (PARI) x='x+O('x^50); Vec((1+15*x)/(1-2*x-7*x^2)) \\ G. C. Greubel, Aug 11 2017 CROSSREFS Cf. A164703, A164603. Sequence in context: A201705 A165668 A269425 * A078847 A201028 A328022 Adjacent sequences: A164599 A164600 A164601 * A164603 A164604 A164605 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Aug 23 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 29 19:01 EDT 2023. Contains 361599 sequences. (Running on oeis4.)