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

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Pisot sequences

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).

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 *)

Prog

(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
(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

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A164033 A020728 A107979 * A231134 A370479 A038112

Adjacent sequences: A020998 A020999 A021000 * A021002 A021003 A021004

Keyword

nonn

Author

R. K. Guy

Status

approved