OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT], 2016.
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,0,1,-1).
FORMULA
G.f.: (-4*x^5+x^4+x^3-3*x^2-2*x+6)/((1-x)*(1-x-x^2-x^5)) (conjectured). - Ralf Stephan, May 12 2004
a(n) = 2*a(n-1)-a(n-3)+a(n-5)-a(n-6) for n>5 (conjectured). - Colin Barker, Jun 05 2016
Theorem: E(6,10) satisfies a(n) = 2 a(n - 1) - a(n - 3) + a(n - 5) - a(n - 6) for n >= 6. Proved using the PtoRv program of Ekhad-Sloane-Zeilberger. This shows that the above conjectures are correct. - N. J. A. Sloane, Sep 10 2016
MATHEMATICA
LinearRecurrence[{2, 0, -1, 0, 1, -1}, {6, 10, 17, 29, 49, 83}, 30] (* Jinyuan Wang, Mar 10 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved