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A253072 The subsequence A253071(2^n-1). 2
1, 7, 21, 95, 333, 1319, 4837, 18447, 68733, 259447, 972565, 3661535, 13756333, 51754567, 194586181, 731919279, 2752461533, 10352254743, 38932913525, 146424889471, 550683608589, 2071066796007, 7789015542949, 29293584500047, 110169505843517, 414334209685687 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A253071 is the Run Length Transform of this sequence.

A253072(2^k-1) = A050476(2^k-1), 0<=k<=3. This is just a coincidence, since it fails at m=4. - Omar E. Pol, Feb 01 2015; N. J. A. Sloane, Feb 20 2015

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, 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 (6,-5,-24,44,-8).

FORMULA

G.f.: -(-1-t+16*t^2-28*t^3+8*t^4)/(1-6*t+5*t^2+24*t^3-44*t^4+8*t^5).

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*y)+1/x+1/y+y+x/y+x+x*y;

OddCA2(f25, 8);

MATHEMATICA

LinearRecurrence[{6, -5, -24, 44, -8}, {1, 7, 21, 95, 333}, 26] (* Jean-François Alcover, Nov 27 2017 *)

PROG

(PARI) Vec(-(8*x^4-28*x^3+16*x^2-x-1)/(8*x^5-44*x^4+24*x^3+5*x^2-6*x+1) + O(x^30)) \\ Colin Barker, Jul 16 2015

CROSSREFS

Cf. A253067, A253068, A253071, A050476.

Sequence in context: A164544 A100025 A121157 * A261854 A219152 A038184

Adjacent sequences:  A253069 A253070 A253071 * A253073 A253074 A253075

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 31 2015

STATUS

approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)