Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
A020717
Pisot sequences L(6,9), E(6,9).
3
6, 9, 14, 22, 35, 56, 90, 145, 234, 378, 611, 988, 1598, 2585, 4182, 6766, 10947, 17712, 28658, 46369, 75026, 121394, 196419, 317812, 514230, 832041, 1346270, 2178310, 3524579, 5702888, 9227466, 14930353, 24157818, 39088170, 63245987, 102334156, 165580142
OFFSET
0,1
REFERENCES
Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.
LINKS
Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
FORMULA
a(n) = Fibonacci(n+5)+1 = A001611(n+5).
a(n) = 2*a(n-1) - a(n-3).
a(n) = A020706(n+1). - R. J. Mathar, Oct 25 2008
MATHEMATICA
Table[Fibonacci[n + 5] + 1, {n, 0, 36}] (* Michael De Vlieger, Jul 27 2016 *)
PROG
(PARI) pisotE(nmax, a1, a2) = {
a=vector(nmax); a[1]=a1; a[2]=a2;
for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));
a
}
pisotE(50, 6, 9) \\ Colin Barker, Jul 27 2016
CROSSREFS
Subsequence of A001611, A048577.
See A008776 for definitions of Pisot sequences.
Pairwise sums of A018910.
Sequence in context: A316019 A316020 A300573 * A196993 A303162 A242042
KEYWORD
nonn,easy
STATUS
approved