A282180 - OEIS

A282180

a(n+1) = a(n)*(a(n)^2 - 3) with a(0) = 8.

8, 488, 116212808, 1569502402942700328379688, 3866214585126515728777536857817155683642224883875510905654220958052649608

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OFFSET

0,1

LINKS

E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644-646.

FORMULA

a(n) = (4 + sqrt(15))^(3^n) + (4 - sqrt(15))^(3^n). - Bruno Berselli, Feb 10 2017

a(n) = -2*cos(3^n * arccos(-4)). - Daniel Suteu, Feb 10 2017

MATHEMATICA

RecurrenceTable[{a[0] == 8, a[n] == a[n-1]^3 - 3 a[n-1]}, a, {n, 8}]

PROG

(Magma) [n eq 1 select 8 else Self(n-1)^3 - 3*Self(n-1): n in [1..6]];

CROSSREFS

Cf. similar sequences with initial value k: A001999 (k=3), A219160 (k=4), A219161 (k=5), A112845 (k=6), A002000 (k=7), this sequence (k=8), A282181 (k=9), A006242 (k=10), A006243 (k=198).

KEYWORD

nonn

AUTHOR

STATUS

approved