A267531 - OEIS

%I #25 Feb 16 2025 08:33:29

%S 0,2,5,9,13,18,23,29,35,42,49,57,65,74,83,93,103,114,125,137,149,162,

%T 175,189,203,218,233,249,265,282,299,317,335,354,373,393,413,434,455,

%U 477,499,522,545,569,593,618,643,669,695,722,749,777,805,834,863,893

%N Total number of OFF (white) cells after n iterations of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A267531/b267531.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%F Conjectures from _Colin Barker_, Jan 17 2016: (Start)

%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 4.

%F G.f.: x*(2+x-x^2-x^3) / ((1-x)^3*(1+x)).

%F (End)

%F Conjecture: a(n) = a(n-1) + A004526(n+5) for n > 1. - _J. Stauduhar_, Oct 21 2017

%t rule=141; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc,k]],{k,1,rows}] (* Number of White cells through stage n *)

%Y Cf. A267525, A267530.

%K nonn

%O 0,2

%A _Robert Price_, Jan 16 2016