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 (0,10001,0,-10000).
FORMULA
From Colin Barker, Dec 28 2015 and Apr 15 2019: (Start)
a(n) = (19*(-1)^n+10^(2*n+1)-(-1)^n*10^(2*n+1)-1)/18.
a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.
G.f.: (1+110*x-10000*x^2+11000*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
a(n) = (10*100^n - 10)/9 for odd n; a(n) = 1 for even n. - Karl V. Keller, Jr., Aug 31 2021
E.g.f.: cosh(x) + 10*(sinh(100*x) - sinh(x))/9. - Stefano Spezia, Sep 02 2021
MATHEMATICA
rule=15; 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 - 10)//9 if n%2 else 1 for n in range(50)]) # Karl V. Keller, Jr., Aug 31 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 26 2015
STATUS
approved