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 A061021 a(n) = a(n-1)*a(n-2) - a(n-3) with a(0) = a(1) = a(2) = 3. 4
 3, 3, 3, 6, 15, 87, 1299, 112998, 146784315, 16586334025071, 2434613678231239448367, 40381315689150066251526220641224742, 98312903521778500654864668915856114278134197773017871243 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Any three consecutive terms are a solution to the Diophantine equation x^2 + y^2 + z^2 = xyz. LINKS Harry J. Smith, Table of n, a(n) for n = 0..17 Loren C. Larson, Solution to Problem Proposal 701, College Mathematics Journal 33 (2002), pp. 241-242. Edward T. H. Wang, Problem Proposal 701, College Mathematics Journal 32 (2001), p. 211. FORMULA From Jon E. Schoenfield, May 12 2019: (Start) It appears that, for n >= 1,   a(n) = ceiling(e^(c0*phi^n - c1/(-phi)^n)) where   phi = (1 + sqrt(5))/2,    c0 = 0.4004033011137849744572073756789830081726425559860...    c1 = 0.2798639753144007577581523025628820390768226527315... (End) MATHEMATICA RecurrenceTable[{a[n] == a[n - 1] a[n - 2] - a[n - 3], a[0] == a[1] == a[2] == 3}, a, {n, 0, 12}] (* Michael De Vlieger, Aug 21 2016 *) PROG (PARI) for (n=0, 17, if (n>2, a=a1*a2 - a3; a3=a2; a2=a1; a1=a, if (n==0, a=a3=3, if (n==1, a=a2=3, a=a1=3))); write("b061021.txt", n, " ", a)) \\ Harry J. Smith, Jul 16 2009 (Haskell) a061021 n = a061021_list !! n a061021_list = 3 : 3 : 3 : zipWith (-) (tail \$ zipWith (*) (tail a061021_list) a061021_list) a061021_list -- Reinhard Zumkeller, Mar 25 2015 CROSSREFS Cf. A022405, A061292, A072878, A072879, A072880, A074394, A178768. Sequence in context: A081848 A079988 A212091 * A126608 A088195 A131757 Adjacent sequences:  A061018 A061019 A061020 * A061022 A061023 A061024 KEYWORD easy,nonn AUTHOR Stephen G. Penrice (spenrice(AT)ets.org), May 23 2001 EXTENSIONS More terms from Erich Friedman, Jun 03 2001 Name clarified by Petros Hadjicostas, May 11 2019 STATUS approved

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Last modified August 24 14:53 EDT 2019. Contains 326295 sequences. (Running on oeis4.)