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A048584 Pisot sequence L(5,7). 3

%I #16 Dec 30 2023 23:47:47

%S 5,7,10,15,23,36,57,91,146,235,379,612,989,1599,2586,4183,6767,10948,

%T 17713,28659,46370,75027,121395,196420,317813,514231,832042,1346271,

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

%N Pisot sequence L(5,7).

%C a(n)= BA^(n)B(1), n>=0, with compositions of Wythoff's complementary A(n):=A000201(n) and B(n)=A001950(n) sequences. See the W. Lang link under A135817 for the Wythoff representation of numbers (with A as 1 and B as 0 and the argument 1 omitted). E.g. 5=`00`, 7=`010`, 10=`0110`, 15=`01110`,..., in Wythoff code.

%H Colin Barker, <a href="/A048584/b048584.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = Fib(n+4)+2. a(n) = 2a(n-1) - a(n-3).

%F a(n)=A020743(n-1), n>0. - _R. J. Mathar_, Oct 15 2008

%t LinearRecurrence[{2,0,-1},{5,7,10},40] (* _Harvey P. Dale_, Oct 02 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, 5, 7) \\ _Colin Barker_, Aug 07 2016

%Y Subsequence of A018910. See A008776 for definitions of Pisot sequences.

%K nonn

%O 0,1

%A _David W. Wilson_

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)