A277089 - OEIS

%I #12 Oct 03 2016 03:42:17

%S 6,15,38,97,248,635,1626,4164,10664,27311,69945,179134,458775,1174956,

%T 3009148,7706648,19737289,50548641,129458768,331553377,849132458,

%U 2174690356,5569541124,14264002343,36531153701,93558957622,239611336203,613662164440,1571633704952

%N Pisot sequences L(6,15), S(6,15).

%H Ilya Gutkovskiy, <a href="/A277089/a277089_1.pdf">Pisot sequences L(x,y)</a>

%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>

%F a(n) = ceiling(a(n-1)^2/a(n-2)), a(0) = 6, a(1) = 15.

%F a(n) = floor(a(n-1)^2/a(n-2)+1), a(0) = 6, a(1) = 15.

%F Conjectures: (Start)

%F G.f.: (6 - 3*x - x^2 - 2*x^3 + x^4 + 3*x^5 - 5*x^6)/((1 - x)*(1 - 2 x - x^2 - x^3 - 2*x^6)).

%F a(n) = 3*a(n-1) - a(n-2) - a(n-4) + 2*a(n-6) - 2*a(n-7). (End)

%t RecurrenceTable[{a[0] == 6, a[1] == 15, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 28}]

%t RecurrenceTable[{a[0] == 6, a[1] == 15, a[n] == Floor[a[n - 1]^2/a[n - 2] + 1]}, a, {n, 28}]

%Y Cf. See A008776 for definitions of Pisot sequences.

%Y Cf. A020717, A048585, A048586, A048587.

%K nonn,easy

%O 0,1

%A _Ilya Gutkovskiy_, Sep 29 2016