The OEIS is supported by the many generous donors to the OEIS 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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A106567 a(n) = 5*a(n-1) + 4*a(n-2), with a(0) = 4, a(1) = 4. 1
 0, 4, 20, 116, 660, 3764, 21460, 122356, 697620, 3977524, 22678100, 129300596, 737215380, 4203279284, 23965257940, 136639406836, 779058065940, 4441847957044, 25325472048980, 144394752073076, 823275648561300, 4693957251098804, 26762888849739220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,4). FORMULA a(n) = 4*A015537(n). From Chai Wah Wu, Mar 21 2018: (Start) a(n) = 5*a(n-1) + 4*a(n-2) for n > 1. G.f.: 4*x/(1 - 5*x - 4*x^2). (End) a(n) = 4*(p^n - q^n)/(p - q), where 2*p = 5 + sqrt(41), 2*q = 5 - sqrt(41). - G. C. Greubel, Sep 06 2021 MATHEMATICA CoefficientList[Series[4*x/(1-5*x-4*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 22 2018 *) PROG (Magma) I:=[0, 4]; [n le 2 select I[n] else 5*Self(n-1) +4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Mar 22 2018 (PARI) a(n) = (([0, 4; 1, 5]^n)*[0, 1]~)[1]; \\ Michel Marcus, Mar 22 2018 (Sage) def A106567_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( 4*x/(1-5*x-4*x^2) ).list() A106567_list(30) # G. C. Greubel, Sep 06 2021 CROSSREFS Cf. A015537. Sequence in context: A192924 A258664 A231539 * A077445 A085458 A085456 Adjacent sequences: A106564 A106565 A106566 * A106568 A106569 A106570 KEYWORD nonn,easy,less AUTHOR Roger L. Bagula, May 30 2005 EXTENSIONS Edited by N. J. A. Sloane, Apr 30 2006 New name after Chai Wah Wu, by Bruno Berselli, Mar 22 2018 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 December 2 18:40 EST 2022. Contains 358510 sequences. (Running on oeis4.)