OFFSET
0,2
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 (0,10101,0,-1010100,0,1000000).
FORMULA
From Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)
a(n) = 10101*a(n-2) - 1010100*a(n-4) + 1000000*a(n-6) for n>5.
G.f.: (1+10*x-10000*x^2+1000000*x^3-1100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).
(End)
a(n) = (10*100^n - (1000*10^n-1)/11 - 1)/9 for odd n; a(n) = (100*10^n-1)/99 for even n. - Karl V. Keller, Jr., Aug 29 2021
MATHEMATICA
rule=13; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *)
PROG
(Python) print([(10*100**n - (1000*10**n-1)//11 - 1)//9 if n%2 else (100*10**n-1)//99 for n in range(50)]) # Karl V. Keller, Jr., Aug 29 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 26 2015
STATUS
approved