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

0,4

Comments

Run length transform gives A246035. - N. J. A. Sloane, Feb 26 2015

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).

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)).

Mathematica

LinearRecurrence[{3, 6, -8}, {0, 1, 1}, 25] (* Jean-François Alcover, Jan 09 2019 *)

Prog

(Magma) [1/9-(2/9)*(-2)^n+(1/9)*4^n: n in [0..35]]; // Vincenzo Librandi, Aug 09 2011
(PARI) concat (0, Vec(x*(1-2*x)/((1-x)*(1+2*x)*(1-4*x)) + O(x^30))) \\ Michel Marcus, Mar 04 2015

Crossrefs

Cf. A001045, A246035. First differences give (apart from signs) A083086.

Sequence in context: A108570 A092769 A263951 * A227078 A146365 A146373

Adjacent sequences: A139815 A139816 A139817 * A139819 A139820 A139821

Keyword

nonn,easy

Author

Paul Curtz, May 17 2008

Extensions

More terms from R. J. Mathar, Dec 12 2009

Status

approved