A278681 Pisot sequence T(3,16).
3, 16, 85, 451, 2392, 12686, 67280, 356818, 1892376, 10036172, 53226604, 282286052, 1497097488, 7939821584, 42108658448, 223322287224, 1184384537744, 6281355751296, 33313023614352, 176674843181968, 936990907061504, 4969309405367264, 26354616443092800, 139771093164846816, 741272730213321216, 3931322622695991104
Offset: 0
Programs
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Mathematica
RecurrenceTable[{a[0] == 3, a[1] == 16, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 25}]
Formula
a(n) = floor(a(n-1)^2/a(n-2)), a(0) = 3, a(1) = 16.
Conjectures: (Start)
G.f.: (3 - 2*x + x^2 - x^3)/(1 - 6*x + 4*x^2 - 2*x^3 + 2*x^4).
a(n) = 6*a(n-1) - 4*a(n-2) + 2*a(n-3) - 2*a(n-4). (End)