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

0,1

Links

Table of n, a(n) for n=0..25.

Index entries for Pisot sequences

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)

Mathematica

RecurrenceTable[{a[0] == 3, a[1] == 16, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 25}]

Crossrefs

Cf. A008776 for definitions of Pisot sequences.

Cf. A010920, A018920.

Sequence in context: A076279 A056369 A056360 * A224869 A163604 A151329

Adjacent sequences: A278678 A278679 A278680 * A278682 A278683 A278684

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Nov 26 2016

Status

approved