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
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.
S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT] (2016)
Index entries for linear recurrences with constant coefficients, signature (6, 1, 3).
FORMULA
Theorem: a(n) = 6 a(n - 1) + a(n - 2) + 3 a(n - 3). (Conjectured by Colin Barker, Jun 05 2016. Proved using the PtoRv program of Ekhad-Sloane-Zeilberger.) - N. J. A. Sloane, Sep 09 2016
G.f.: (4+x+2*x^2) / (1-6*x-x^2-3*x^3). (Follows from the recurrence.)
MATHEMATICA
RecurrenceTable[{a[0] == 4, a[1] == 25, a[n] == Floor[a[n - 1]^2/a[n - 2] + 1/2]}, a, {n, 0, 25}] (* Bruno Berselli, Sep 03 2013 *)
PROG
(Magma) Exy:=[4, 25]; [n le 2 select Exy[n] else Floor(Self(n-1)^2/Self(n-2)+1/2): n in [1..25]]; // Bruno Berselli, Sep 03 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Bruno Berselli, Sep 03 2013
STATUS
approved