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 A255442 a(n) = A255304(2^n-1). 2
 1, 5, 15, 51, 153, 477, 1431, 4347, 13041, 39285, 117855, 354051, 1062153, 3187917, 9563751, 28695627, 86086881, 258273765, 774821295, 2324503251, 6973509753, 20920647357, 62761942071, 188286180507, 564858541521, 1694576687445, 5083730062335, 15251193375651, 45753580126953, 137260749946797 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, 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 [math.CO], 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 linear recurrences with constant coefficients, signature (3,3,-9). FORMULA G.f.: (1+3*x)*(1-x) / ((1-3*x)*(1-3*x^2)). From Colin Barker, Feb 04 2017: (Start) a(n) = 2*3^n - 3^((n-1)/2)/2*(1-(-1)^n+sqrt(3) + (-1)^n*sqrt(3)). a(n) = 3*a(n-1) + 3*a(n-2) - 9*a(n-3) for n>2. (End) MATHEMATICA A255442[n_] := SeriesCoefficient[(1 + 3*x)*(1 - x)/((1 - 3*x)*(1 - 3*x^2)), {x, 0, n}]; Array[A255442, 30, 0] (* JungHwan Min, Sep 29 2016 *) A255442L[n_] := CoefficientList[Series[(1 + 3*x)*(1 - x)/((1 - 3*x)*(1 - 3*x^2)), {x, 0, n}], x]; A255442L[29] (* JungHwan Min, Sep 29 2016 *) PROG (PARI) Vec((1+3*x)*(1-x) / ((1-3*x)*(1-3*x^2)) + O(x^30)) \\ Colin Barker, Feb 04 2017 CROSSREFS Cf. A255304. Sequence in context: A014274 A120825 A199985 * A149576 A149577 A149578 Adjacent sequences:  A255439 A255440 A255441 * A255443 A255444 A255445 KEYWORD nonn,easy AUTHOR N. J. A. Sloane and Doron Zeilberger, Feb 23 2015 STATUS approved

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Last modified March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)