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 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-François 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_

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