OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.
D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
S. B. Ekhad, N. J. A. Sloane, and D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT], 2016.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (6, 6).
FORMULA
Conjecture: a(n) = 6*a(n-1) + 6*a(n-2), n > 1; a(0)=8, a(1)=55; g.f.: (8+7x)/(1-6x-6x^2). - Philippe Deléham, Nov 19 2008
Theorem: a(n) = 6*a(n-1) + 6*a(n-2) for n >= 2. Proved using the PtoRv program of Ekhad-Sloane-Zeilberger, and implies the above conjectures. - N. J. A. Sloane, Sep 09 2016
MATHEMATICA
a[0] = 8; a[1] = 55; a[n_] := a[n] = Floor[a[n - 1]^2/a[n - 2] + 1/2]; Table[a[n], {n, 0, 20}] (* Michael De Vlieger, Jul 27 2016 *)
LinearRecurrence[{6, 6}, {8, 55}, 30] (* Harvey P. Dale, Mar 06 2022 *)
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, 8, 55) \\ Colin Barker, Jul 27 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved