

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
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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 MetaAlgorithm for Creating Fast Algorithms for Counting ON Cells in OddRule Cellular Automata, arXiv:1503.01796 [math.CO], 2015; see also the Accompanying Maple Package.
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, OddRule 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(n1)+6a(n2)8a(n3).
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*(12*x)/((1x)*(1+2*x)*(14*x)).


MATHEMATICA

LinearRecurrence[{3, 6, 8}, {0, 1, 1}, 25] (* JeanFrançois 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*(12*x)/((1x)*(1+2*x)*(14*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



