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..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Dec 07 2015 and Apr 16 2019: (Start)
a(n) = (2*n^2+12*n-(-1)^n+1)/4 for n>0.
a(n) = (n^2+6*n)/2 for n>1 and even.
a(n) = (n^2+6*n+1)/2 for n odd.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.
G.f.: (1+2*x-x^4) / ((1-x)^3*(1+x)).
(End)
MATHEMATICA
rule = 94; rows = 30; Table[Total[Take[Table[Total[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}], k]], {k, 1, rows}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 06 2015
STATUS
approved