A265284 Total number of ON (black) cells after n iterations of the "Rule 94" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 8, 14, 20, 28, 36, 46, 56, 68, 80, 94, 108, 124, 140, 158, 176, 196, 216, 238, 260, 284, 308, 334, 360, 388, 416, 446, 476, 508, 540, 574, 608, 644, 680, 718, 756, 796, 836, 878, 920, 964, 1008, 1054, 1100, 1148, 1196, 1246, 1296, 1348, 1400, 1454

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

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

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

Cf. A118102.

Sequence in context: A232996 A317292 A276221 * A055507 A343880 A121896

Adjacent sequences: A265281 A265282 A265283 * A265285 A265286 A265287

Keyword

nonn,easy

Author

Robert Price, Dec 06 2015

Status

approved