OFFSET
0,2
REFERENCES
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for linear recurrences with constant coefficients, signature (0,21,0,-84,0,64).
FORMULA
From Colin Barker, Dec 23 2015 and Apr 13 2019: (Start)
a(n) = 21*a(n-2) - 84*a(n-4) + 64*a(n-6) for n>5.
G.f.: (1+2*x-17*x^2+65*x^3+16*x^4-112*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).
(End)
a(n) = 2^n = A000079(n) for even n>=0; a(n) = 2*4^n - 5*2^(n-1) - 1 = A188530(n) for odd n. - Karl V. Keller, Jr., Jun 19 2021
MATHEMATICA
rule = 5; rows = 30; Table[FromDigits[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]], 2], {k, 1, rows}]
PROG
(Python) print([2*4**n -5*2**(n-1) -1 if n%2 else 2**n for n in range(30)]) # Karl V. Keller, Jr., Jun 20 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 22 2015
STATUS
approved