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A253068
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The subsequence A253066(2^n-1).
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4
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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
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OFFSET
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0,2
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COMMENTS
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A253066 is the Run Length Transform of this sequence.
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LINKS
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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
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FORMULA
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G.f.: (1+3x+4x^2)/((1-x)(1+2x)(1-4x)).
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MAPLE
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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
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PROG
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(PARI) a(n) = ((-2)^n+4^(2+n)-8)/9 \\ Colin Barker, Jul 16 2015
(PARI) Vec((4*x^2+3*x+1)/((x-1)*(2*x+1)*(4*x-1)) + O(x^30)) \\ Colin Barker, Jul 16 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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