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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, 125099997105721, 500399943683641

(list; graph; refs; listen; history; text; internal format)

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)).

E.g.f.: exp(x)*(1 + exp(3*x) - 2*exp(-3*x))/9. - Elmo R. Oliveira, Mar 10 2026

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