A139818 Squares of Jacobsthal numbers.
0, 1, 1, 9, 25, 121, 441, 1849, 7225, 29241, 116281, 466489, 1863225, 7458361, 29822521, 119311929, 477204025, 1908903481, 7635439161, 30542106169, 122167725625, 488672300601, 1954686406201, 7818751217209, 31274993684025
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata, arXiv:1503.01796 [math.CO], 2015; see also the Accompanying Maple Package.
- Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, Odd-Rule Cellular Automata on the Square Grid, arXiv:1503.04249, 2015.
- N. J. A. Sloane, On the No. of ON Cells in Cellular Automata, Video of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Feb. 05 2015: Part 1, Part 2
- N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.
- Index entries for sequences related to cellular automata
- Index entries for linear recurrences with constant coefficients, signature (3,6,-8).
Programs
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Magma
[1/9-(2/9)*(-2)^n+(1/9)*4^n: n in [0..35]]; // Vincenzo Librandi, Aug 09 2011
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Mathematica
LinearRecurrence[{3, 6, -8}, {0, 1, 1}, 25] (* Jean-François Alcover, Jan 09 2019 *) -
PARI
concat (0, Vec(x*(1-2*x)/((1-x)*(1+2*x)*(1-4*x)) + O(x^30))) \\ Michel Marcus, Mar 04 2015
Formula
a(n) = 3*a(n-1) + 6*a(n-2) - 8*a(n-3).
a(n) = (A001045(n))^2.
G.f.: x*(1-2*x)/((1-x)*(1+2*x)*(1-4*x)).
Extensions
More terms from R. J. Mathar, Dec 12 2009
Comments