OFFSET
1,2
LINKS
Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru, Linear divisibility sequences and Salem numbers, arXiv:1709.01995 [math.NT], 2017.
FORMULA
a(n) = round(lambda(7)*alpha(7)^n)
where alpha(t) = (t+sqrt((t-4)*t+8)+sqrt(2)*sqrt(t*(t+sqrt((t-4)*t+8)-2)-4))/4
and lambda(t) = 1/sqrt((t-4)*t+8).
Conjectures from Colin Barker, Dec 17 2017: (Start)
G.f.: x*(1 - x)*(1 + x) / (1 - 7*x + 7*x^2 - 7*x^3 + x^4).
a(n) = 7*a(n-1) - 7*a(n-2) + 7*a(n-3) - a(n-4) for n>4.
(End)
MATHEMATICA
alpha[t_] := (t + Sqrt[(t - 4) t + 8] + Sqrt[2] Sqrt[t (t + Sqrt[(t - 4) t + 8] - 2) - 4])/4;
lambda[t_] := 1/Sqrt[(t - 4) t + 8];
a[n_] := Round[lambda[7] alpha[7]^n] ;
Array[a, 24] (* Jean-François Alcover, Feb 02 2019 *)
PROG
(PARI) alpha(t) = (t+sqrt((t-4)*t+8)+sqrt(2)*sqrt(t*(t+sqrt((t-4)*t+8)-2)-4))/4;
lambda(t) = 1/sqrt((t-4)*t+8);
a(n) = my(ca=alpha(7), cl=lambda(7)); round(cl*ca^n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Sep 08 2017
STATUS
approved