The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A163611 a(n) = ((5 + 2*sqrt(2))*(5 + sqrt(2))^n + (5 - 2*sqrt(2))*(5 - sqrt(2))^n)/2. 3
 5, 29, 175, 1083, 6805, 43141, 274895, 1756707, 11244485, 72040589, 461782735, 2960893803, 18987935125, 121778793781, 781065429935, 5009742042387, 32132915535365, 206105088378749, 1321993826474095, 8479521232029723 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Binomial transform of A163610. Fifth binomial transform of A163888. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (10,-23). FORMULA a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 29. G.f.: (5-21*x)/(1-10*x+23*x^2). E.g.f.: exp(5*x)*( 5*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 29 2017 MATHEMATICA LinearRecurrence[{10, -23}, {5, 29}, 50] (* G. C. Greubel, Jul 29 2017 *) PROG (MAGMA) Z:= PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((5+2*r)*(5+r)^n+(5-2*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 06 2009 (PARI) x='x+O('x^50); Vec((5-21*x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Jul 29 2017 CROSSREFS Cf. A163610, A163888. Sequence in context: A272802 A083066 A327557 * A160906 A163073 A190802 Adjacent sequences:  A163608 A163609 A163610 * A163612 A163613 A163614 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Aug 06 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 December 5 12:04 EST 2021. Contains 349557 sequences. (Running on oeis4.)