%I #13 Feb 02 2019 10:43:00
%S 1,6,29,144,725,3654,18409,92736,467161,2353350,11855141,59720976,
%T 300847949,1515539334,7634619025,38459844864,193743743089,
%U 975995564166,4916635376621,24767841488400,124769466312581,628533565640646,3166275009522169,15950297619676224,80350567588455625
%N Linear divisibility sequence based on Salem number of order 4 (case t=6, see formula).
%H Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru, <a href="https://arxiv.org/abs/1709.01995">Linear divisibility sequences and Salem numbers</a>, arXiv:1709.01995 [math.NT], 2017.
%F a(n) = round(lambda(6)*alpha(6)^n)
%F where alpha(t) = (t+sqrt((t-4)*t+8)+sqrt(2)*sqrt(t*(t+sqrt((t-4)*t+8)-2)-4))/4
%F and lambda(t) = 1/sqrt((t-4)*t+8).
%F Conjectures from _Colin Barker_, Dec 17 2017: (Start)
%F G.f.: x*(1 - x)*(1 + x) / (1 - 6*x + 6*x^2 - 6*x^3 + x^4).
%F a(n) = 6*a(n-1) - 6*a(n-2) + 6*a(n-3) - a(n-4) for n>4.
%F (End)
%t alpha[t_] := (t + Sqrt[(t - 4) t + 8] + Sqrt[2] Sqrt[t (t + Sqrt[(t - 4) t + 8] - 2) - 4])/4;
%t lambda[t_] := 1/Sqrt[(t - 4) t + 8];
%t a[n_] := Round[lambda[6] alpha[6]^n] ;
%t Array[a, 25] (* _Jean-François Alcover_, Feb 02 2019 *)
%o (PARI) alpha(t) = (t+sqrt((t-4)*t+8)+sqrt(2)*sqrt(t*(t+sqrt((t-4)*t+8)-2)-4))/4;
%o lambda(t) = 1/sqrt((t-4)*t+8);
%o a(n) = my(ca=alpha(6), cl=lambda(6)); round(cl*ca^n);
%Y Cf. A292035.
%K nonn
%O 1,2
%A _Michel Marcus_, Sep 08 2017