

A253072


The subsequence A253071(2^n1).


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
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OFFSET

0,2


COMMENTS

A253071 is the Run Length Transform of this sequence.
A253072(2^k1) = A050476(2^k1), 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 MetaAlgorithm for Creating Fast Algorithms for Counting ON Cells in OddRule Cellular Automata, arXiv:1503.01796, 2015; see also the Accompanying Maple Package.
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, OddRule 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.: (1t+16*t^228*t^3+8*t^4)/(16*t+5*t^2+24*t^344*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] (* JeanFrançois Alcover, Nov 27 2017 *)


PROG

(PARI) Vec((8*x^428*x^3+16*x^2x1)/(8*x^544*x^4+24*x^3+5*x^26*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



