login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A018910 Pisot sequence L(4,5). 10

%I

%S 4,5,7,10,15,23,36,57,91,146,235,379,612,989,1599,2586,4183,6767,

%T 10948,17713,28659,46370,75027,121395,196420,317813,514231,832042,

%U 1346271,2178311,3524580,5702889,9227467,14930354,24157819,39088171,63245988,102334157,165580143

%N Pisot sequence L(4,5).

%H Colin Barker, <a href="/A018910/b018910.txt">Table of n, a(n) for n = 0..1000</a>

%H D. W. Boyd, <a href="https://www.researchgate.net/profile/David_Boyd7/publication/262181133_Linear_recurrence_relations_for_some_generalized_Pisot_sequences_-_annotated_with_corrections_and_additions/links/00b7d536d49781037f000000.pdf">Linear recurrence relations for some generalized Pisot sequences</a>, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -1).

%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>

%F a(n) = Fib(n+3)+2 = A020743(n-2) = A157725(n+3); a(n) = 2a(n-1) - a(n-3).

%F G.f.: -(-4+3*x+3*x^2)/(x-1)/(x^2+x-1) = -2/(x-1)+(-x-2)/(x^2+x-1) . - _R. J. Mathar_, Nov 23 2007

%F a(n)=2+((5+2r5)/5)((1+r5)/2)^n+((5-2r5)/5)((1-r5)/2)^n, where r5 = sqrt(5).

%F - _Paolo P. Lava_, Jun 10 2008

%t LinearRecurrence[{2, 0, -1}, {4, 5, 7}, 40] (* _Jean-Fran├žois Alcover_, Dec 12 2016 *)

%o (PARI) pisotL(nmax, a1, a2) = {

%o a=vector(nmax); a[1]=a1; a[2]=a2;

%o for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));

%o a

%o }

%o pisotL(50, 4, 5) \\ _Colin Barker_, Aug 07 2016

%Y See A008776 for definitions of Pisot sequences.

%K nonn,easy

%O 0,1

%A _R. K. Guy_

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 09:21 EST 2019. Contains 329877 sequences. (Running on oeis4.)