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A213680 a(n) = 2*a(n-1)^2/3-3 with a(0)=6. 0
6, 21, 291, 56451, 2124476931, 3008934820234119171, 6035792501611554034238453484153151491, 24287194081673507672666338605180770497437885188248737771493963111463682051 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..7.

FORMULA

a(n) = 3*cosh(2^n*arccosh(2)).

a(n) = 3*A002812(n). [Giovanni Resta, Mar 04 2013]

EXAMPLE

a(1) = 2*a(0)^2/3-3 = 2*6^2/3-3 = 21,

a(2) = 2*a(1)^2/3-3 = 2*21^2/3-3 = 291,

a(3) = 2*a(2)^2/3-3 = 2*291^2/3-3 = 2*84681/3-3 = 56451.

Or, by the first formula:

a(3) = 3*cosh(2^3*arccosh(2)) = 56451,

a(4) = 3*cosh(2^4*arccosh(2)) = 2124476931.

PROG

(Sage)

var('x')

p=2*x^2/3-3

s=[6]

for i in [0..8]:

    s=s+[p(s[i])]

show(s)

CROSSREFS

Cf. A002812.

Sequence in context: A131960 A244299 A143049 * A164643 A190275 A261844

Adjacent sequences:  A213677 A213678 A213679 * A213681 A213682 A213683

KEYWORD

nonn

AUTHOR

Jose Eduardo Blazek, Mar 04 2013

STATUS

approved

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Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)