A021001 Pisot sequence P(2,9).

2, 9, 40, 178, 792, 3524, 15680, 69768, 310432, 1381264, 6145920, 27346208, 121676672, 541399104, 2408949760, 10718597248, 47692288512, 212206348544, 944209971200, 4201252581888, 18693430269952, 83176226243584, 370091765514240, 1646719514544128

Offset: 0

Author

R. K. Guy

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for Pisot sequences

Crossrefs

See A008776 for definitions of Pisot sequences.

Programs

Magma

Iv:=[2, 9]; [n le 2 select Iv[n] else Ceiling(Self(n-1)^2/Self(n-2)-1/2): n in [1..30]]; // Bruno Berselli, Feb 04 2016

Mathematica

RecurrenceTable[{a[0] == 2, a[1] == 9, a[n] == Ceiling[a[n - 1]^2/a[n - 2]-1/2]}, a, {n, 0, 30}] (* Bruno Berselli, Feb 04 2016 *)

PARI

lista(nn) = {print1(x = 2, ", ", y = 9, ", "); for (n=1, nn, z = ceil(y^2/x -1/2); print1(z, ", "); x = y; y = z;);} \\ Michel Marcus, Feb 04 2016

Formula

Pisot sequence P(x, y): a(0) = x, a(1) = y, a(n) = roundDown(a(n-1)^2/a(n-2)) = ceiling(a(n-1)^2/a(n-2) - 1/2).

Appears to satisfy a(n) = 4*a(n-1) + 2*a(n-2).