This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A266287 Total number of OFF (white) cells after n iterations of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1
 0, 2, 5, 8, 14, 18, 27, 32, 44, 50, 65, 72, 90, 98, 119, 128, 152, 162, 189, 200, 230, 242, 275, 288, 324, 338, 377, 392, 434, 450, 495, 512, 560, 578, 629, 648, 702, 722, 779, 800, 860, 882, 945, 968, 1034, 1058, 1127, 1152, 1224, 1250, 1325, 1352, 1430 (list; graph; refs; listen; history; text; internal format)
 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 28 2015 and Apr 14 2019: (Start) a(n) = (2*n^2+5*n+(-1)^n*(n-1)+1)/4. a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4. G.f.: x*(2+3*x-x^2) / ((1-x)^3*(1+x)^2). (End) MATHEMATICA rule=13; 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 *) CROSSREFS Cf. A266282. Sequence in context: A191109 A190105 A295400 * A111711 A095348 A215725 Adjacent sequences:  A266284 A266285 A266286 * A266288 A266289 A266290 KEYWORD nonn,easy AUTHOR Robert Price, Dec 26 2015 EXTENSIONS Conjectures from Colin Barker, Apr 14 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 21:42 EST 2019. Contains 329809 sequences. (Running on oeis4.)