A253068 The subsequence A253066(2^n-1).
1, 6, 28, 112, 456, 1816, 7288, 29112, 116536, 465976, 1864248, 7456312, 29826616, 119303736, 477220408, 1908870712, 7635504696, 30541975096, 122167987768, 488671776312, 1954687454776, 7818749120056, 31274997878328, 125099988717112, 500399960460856, 2001599830658616, 8006399345004088, 32025597335277112, 128102389430586936
Offset: 0
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 sequences related to cellular automata
- Index entries for linear recurrences with constant coefficients, signature (3,6,-8).
Crossrefs
Cf. A253066.
Programs
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Maple
OddCA2:=proc(f,M) local n,a,i,f2,g,p; f2:=simplify(expand(f)) mod 2; p:=1; g:=f2; for n from 1 to M do p:=expand(p*g) mod 2; print(n,nops(p)); g:=expand(g^2) mod 2; od: return; end; f25:=1/x+1+x+1/y+y/x+x*y; OddCA2(f25,8);
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Mathematica
LinearRecurrence[{3, 6, -8}, {1, 6, 28}, 29] (* Jean-François Alcover, Nov 23 2017 *) -
PARI
a(n) = ((-2)^n+4^(2+n)-8)/9 \\ Colin Barker, Jul 16 2015
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PARI
Vec((4*x^2+3*x+1)/((x-1)*(2*x+1)*(4*x-1)) + O(x^30)) \\ Colin Barker, Jul 16 2015
Formula
G.f.: (1+3x+4x^2)/((1-x)(1+2x)(1-4x)).
a(n) = ((-2)^n+4^(2+n)-8)/9. - Colin Barker, Jul 16 2015
Comments