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A246036 G.f.: (1+4*x)/((1+2*x)*(1-4*x)). 6
1, 6, 20, 88, 336, 1376, 5440, 21888, 87296, 349696, 1397760, 5593088, 22368256, 89481216, 357908480, 1431666688, 5726601216, 22906535936, 91625881600, 366504050688, 1466015154176, 5864062713856, 23456246661120, 93824995033088, 375299963355136, 1501199886974976, 6004799480791040, 24019198057381888 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also, fourth moments of Rudin-Shapiro polynomials (see Doche, Doche-Habsieger, Ekhad papers). - Doron Zeilberger, Apr 15 2016.

REFERENCES

Doche, Christophe. "Even moments of generalized Rudin-Shapiro polynomials." Mathematics of computation 74.252 (2005): 1923-1935.

Doche, Christophe, and Laurent Habsieger. "Moments of the Rudin-Shapiro polynomials." Journal of Fourier Analysis and Applications 10.5 (2004): 497-505.

Shalosh B. Ekhad, Explicit Generating Functions, Asymptotics, and More for the First 10 Even Moments of the Rudin-Shapiro Polynomials, Preprint, 2016.

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, 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, 2015

Index entries for sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (2,8).

FORMULA

a(n) = 2*a(n-1) + 8*a(n-2).

a(n) = (4^(1+n)-(-2)^n)/3. - Colin Barker, Aug 22 2014

It appears that a(n) = A054881(n+3)/8. - L. Edson Jeffery, Apr 22 2015

MATHEMATICA

CoefficientList[Series[(1 + 4 x)/((1 + 2 x) (1 - 4 x)), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 22 2014 *)

PROG

(MAGMA) I:=[1, 6]; [n le 2 select I[n] else 2*Self(n-1)+8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 22 2014

(PARI) Vec(-(4*x+1)/((2*x+1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Aug 22 2014

CROSSREFS

Cf. A246037, A054881, A271494, A271495, A271496.

Sequence in context: A255469 A226638 A274071 * A151485 A191424 A200538

Adjacent sequences:  A246033 A246034 A246035 * A246037 A246038 A246039

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 21 2014

STATUS

approved

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