OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Robert Price, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
G.f.: (1+x+2*x^3)/((1-x)^3*(1+x)). - Vincenzo Librandi, Jan 18 2016
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>3. - Vincenzo Librandi, Jan 18 2016
MATHEMATICA
rule=155; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)
LinearRecurrence[{2, 0, -2, 1}, {1, 3, 6, 12}, 50] (* Vincenzo Librandi, Jan 18 2016 *)
PROG
(Magma) I:=[1, 3, 6, 12]; [n le 4 select I[n] else 2*Self(n-1)-2*Self(n-3)+Self(n-4): n in [1..60]]; // Vincenzo Librandi, Jan 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 17 2016
STATUS
approved