OFFSET
0,2
COMMENTS
A253066 is the Run Length Transform of this sequence.
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 linear recurrences with constant coefficients, signature (3,6,-8).
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
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);
MATHEMATICA
LinearRecurrence[{3, 6, -8}, {1, 6, 28}, 29] (* Jean-François Alcover, Nov 23 2017 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane and Doron Zeilberger, Feb 23 2015
STATUS
approved