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A253067
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The subsequence A253065(2^n-1).
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4
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1, 5, 17, 65, 229, 813, 2945, 10513, 37701, 135261, 484609, 1737665, 6229413, 22330829, 80057281, 286996657, 1028861637, 3688409853, 13222664897, 47402353633, 169934149285, 609201913325, 2183946525185, 7829295473489, 28067476697413, 100619943566493
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OFFSET
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0,2
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COMMENTS
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A253065 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+2*x)*(1+2*x+3*x^2+4*x^3)/(1-x-5*x^2-13*x^3-6*x^4-8*x^5).
Examination of the roots of the denominator shows that the ratio of successive terms approaches 3.5849301...
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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;
f24:=1/x+1+x+x/y+x*y;
OddCA2(f24, 8);
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MATHEMATICA
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LinearRecurrence[{1, 5, 13, 6, 8}, {1, 5, 17, 65, 229}, 26] (* Jean-François Alcover, Nov 23 2017 *)
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PROG
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(PARI) Vec(-(2*x+1)*(4*x^3+3*x^2+2*x+1)/(8*x^5+6*x^4+13*x^3+5*x^2+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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