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 A072328 a(n+1) = 2*a(n-2) + a(n-1), with a(0) = 3, a(1) = 0, and a(2) = 2. 1
 3, 0, 2, 6, 2, 10, 14, 14, 34, 42, 62, 110, 146, 234, 366, 526, 834, 1258, 1886, 2926, 4402, 6698, 10254, 15502, 23650, 36010, 54654, 83310, 126674, 192618, 293294, 445966, 678530, 1032554, 1570462, 2389614, 3635570, 5530538, 8414798, 12801678, 19475874 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS With the term indexed as shown, has property that p prime => p divides a(p). a(n) = x^n + y^n + z^n with x, y, z the three roots of x^3 - x - 2. - James R. Buddenhagen, Nov 05 2013 LINKS Matthew Macauley , Jon McCammond, Henning S. Mortveit, Dynamics groups of asynchronous cellular automata, Journal of Algebraic Combinatorics, Vol 33, No 1 (2011), pp. 11-35. Yüksel Soykan, Summing Formulas For Generalized Tribonacci Numbers, arXiv:1910.03490 [math.GM], 2019. Index entries for linear recurrences with constant coefficients, signature (0,1,2). FORMULA e=-1/2+i*sqrt(3)/2, e^2=-1/2-i*sqrt(3)/2, x=(1+sqrt(26/27))^(1/3)+(1-sqrt(26/27))^(1/3), y=e*(1+sqrt(26/27))^(1/3)+(e^2)*(1-sqrt(26/27))^(1/3), z=(e^2)*(1+sqrt(26/27))^(1/3)+e*(1-sqrt(26/27))^(1/3), a(n)=x^n+y^n+z^n. EXAMPLE a(10)=2*a(7)+a(8): 62=2*14+34. MATHEMATICA LinearRecurrence[{0, 1, 2}, {3, 0, 2}, 50] (* T. D. Noe, Nov 05 2013 *) Table[RootSum[-2 - #1 + #1^3 &, #^n &], {n, 0, 40}] (* Eric W. Weisstein, Dec 09 2014 *) CROSSREFS Cf. A001608. Sequence in context: A058544 A112156 A285723 * A135040 A048733 A309973 Adjacent sequences:  A072325 A072326 A072327 * A072329 A072330 A072331 KEYWORD easy,nonn AUTHOR Miklos Kristof, Jul 15 2002 STATUS approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)