A246038 G.f.: (1+2x)(1+2x+4x^2)/(1-3x-8x^3-8x^4).

1, 7, 29, 103, 373, 1407, 5277, 19639, 73157, 272943, 1018157, 3796839, 14159317, 52806751, 196940221, 734469911, 2739138277, 10215390607, 38097452877, 142081224135, 529879903477, 1976142458303, 7369856791005, 27485259393911, 102503957075973, 382279865222383, 1425680525146477, 5316955307198503

Offset

0,2

Comments

This is the subsequence A246039(2^n-1), n >= 0.

Links

Harvey P. Dale, 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 (3, 0, 8, 8).

Maple

-(2*x+1)*(4*x^2+2*x+1)/(8*x^4+8*x^3+3*x-1);

Mathematica

LinearRecurrence[{3, 0, 8, 8}, {1, 7, 29, 103}, 28] (* Jean-François Alcover, Oct 09 2018 *)
CoefficientList[Series[(1+2x)(1+2x+4x^2)/(1-3x-8x^3-8x^4), {x, 0, 30}], x] (* Harvey P. Dale, May 11 2026 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 8, 8, 0, 3]^n*[1; 7; 29; 103])[1, 1] \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Cf. A246039.

Sequence in context: A369805 A227086 A102485 * A049349 A124828 A296646

Adjacent sequences: A246035 A246036 A246037 * A246039 A246040 A246041

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Aug 21 2014

Status

approved