|
|
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.
|
|
LINKS
|
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
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|