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A139818 Squares of Jacobsthal numbers. 7
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 (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). [R. J. Mathar, Dec 12 2009]

FORMULA

a(n) = 3a(n-1)+6a(n-2)-8a(n-3).

a(n) = 1/9-(2/9)*(-2)^n+(1/9)*4^n, with n>=0. - Paolo P. Lava, Jun 12 2008

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-Fran├žois 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

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Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)