OFFSET
0,2
LINKS
Robert Price, Table of n, a(n) for n = 0..1000
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, Jan 13 2016 and Apr 19 2019: (Start)
a(n) = 10001*a(n-2)-10000*a(n-4) for n>8.
G.f.: (1 +110*x -9890*x^2 +10900*x^3 -1089000*x^4 +989000*x^5 -109000000*x^6 +110000000*x^7 -10000000000*x^8) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)).
(End)
a(n) = floor(10*100^n/9) - 11101 for odd n>4; a(n) = 1011111 for even n>4. - Karl V. Keller, Jr., Sep 14 2021
MATHEMATICA
rule=111; 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([1, 110, 111, 1111010, 11111] + [10*100**n//9 - 11101 if n%2 else 1011111 for n in range(5, 50)]) # Karl V. Keller, Jr., Sep 14 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 12 2016
STATUS
approved