A072328 a(n+1) = 2*a(n-2) + a(n-1), with a(0) = 3, a(1) = 0, and a(2) = 2.
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
Offset: 0
Examples
a(10)=2*a(7)+a(8): 62=2*14+34.
Links
- Matthew Macauley , Jon McCammond, and Henning S. Mortveit, Dynamics groups of asynchronous cellular automata, Journal of Algebraic Combinatorics, Vol 33, No 1 (2011), pp. 11-35.
- Souvik Roy, Nazim Fatès, and Sukanta Das, Reversibility of Elementary Cellular Automata with fully asynchronous updating: an analysis of the rules with partial recurrence, hal-04456320 [nlin.CG], [cs], 2024. See p. 17.
- Index entries for linear recurrences with constant coefficients, signature (0,1,2).
Crossrefs
Cf. A001608.
Programs
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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 *)
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.
Extensions
Deleted certain dangerous or potentially dangerous links. - N. J. A. Sloane, Jan 30 2021
Comments