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A021001 Pisot sequence P(2,9). 4
2, 9, 40, 178, 792, 3524, 15680, 69768, 310432, 1381264, 6145920, 27346208, 121676672, 541399104, 2408949760, 10718597248, 47692288512, 212206348544, 944209971200, 4201252581888, 18693430269952, 83176226243584, 370091765514240, 1646719514544128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

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).

Conjecture: a(n) = (2+sqrt(6))^n+(2-sqrt(6))^n+(5/12)*sqrt(6)*((2+sqrt(6))^n-(2-sqrt(6))^n). - Paolo P. Lava, Dec 01 2008

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 A038112 A268039

Adjacent sequences:  A020998 A020999 A021000 * A021002 A021003 A021004

KEYWORD

nonn

AUTHOR

R. K. Guy

STATUS

approved

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Last modified February 21 21:41 EST 2018. Contains 299427 sequences. (Running on oeis4.)