OFFSET
0,2
COMMENTS
Rule 35 also generates this sequence.
LINKS
Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
Index entries for linear recurrences with constant coefficients, signature (0,10011,0,-110010,0,100000).
FORMULA
G.f.: (1+100*x-10001*x^2+109901*x^3+10000*x^4-120000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)). - Colin Barker, Dec 21 2015
a(n) = (10*100^n - 99*10^((n-1)/2) - 1)/9 for odd n; a(n) = 10^(n/2) for even n. - Karl V. Keller, Jr., Aug 26 2021
EXAMPLE
From Michael De Vlieger, Dec 21 2015: (Start)
First 8 rows, replacing leading zeros with ".", the row converted to its binary equivalent at right:
1 = 1
1 0 0 = 100
. . . 1 0 = 10
1 1 1 1 0 0 1 = 1111001
. . . . . . 1 0 0 = 100
1 1 1 1 1 1 1 0 0 1 1 = 11111110011
. . . . . . . . . 1 0 0 0 = 1000
1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 = 111111111100111
(End)
MATHEMATICA
rule = 3; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}]
PROG
(Python) print([(10*100**n - 99*10**((n-1)//2) - 1)//9 if n%2 else 10**(n//2) for n in range(30)]) # Karl V. Keller, Jr., Aug 26 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 20 2015
STATUS
approved