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 A002000 a(n+1) = a(n)*(a(n)^2 - 3) with a(0) = 7. (Formerly M4463 N1892) 3
 7, 322, 33385282, 37210469265847998489922, 51522323599677629496737990329528638956583548304378053615581043535682 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..6 E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644-646. FORMULA From Peter Bala, Feb 01 2017: (Start) a(n) = ((7 + sqrt(45))/2)^(3^n) + ((7 - sqrt(45))/2)^(3^n). a(n) = 2*T(3^n,7/2), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. Product_{n = 0..inf} (1 + 2/(a(n) - 1)) = 3*sqrt(5)/5. Cf. A001999 and A219161. (End) MATHEMATICA RecurrenceTable[{a[0] == 7, a[n] == a[n - 1]^3 - 3 a[n - 1]}, a, {n, 0, 8}] (* Vincenzo Librandi, Feb 09 2017 *) PROG (MAGMA) [n eq 1 select 7 else Self(n-1)^3 - 3*Self(n-1): n in [1..6]]; // Vincenzo Librandi, Feb 09 2017 CROSSREFS Cf. A001999, A219161. Sequence in context: A220278 A163437 A109059 * A092588 A049686 A177019 Adjacent sequences:  A001997 A001998 A001999 * A002001 A002002 A002003 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)