The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A118171 Decimal representation of n-th iteration of the Rule 158 elementary cellular automaton starting with a single black cell. 5
 1, 7, 29, 115, 477, 1843, 7645, 29491, 122333, 471859, 1957341, 7549747, 31317469, 120795955, 501079517, 1932735283, 8017272285, 30923764531, 128276356573, 494780232499, 2052421705181, 7916483719987, 32838747282909, 126663739519795, 525419956526557 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Rule 158 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Index entries for sequences related to cellular automata Index entries for linear recurrences with constant coefficients, signature (0,17,0,-16). FORMULA a(n) = (1/30)*(-16+(-4)^n-10*(-1)^n+55*4^n). From Colin Barker, Oct 08 2015: (Start) a(n) = 17*a(n-2) - 16*a(n-4) for n>3. G.f.: -(4*x^3-12*x^2-7*x-1) / ((x-1)*(x+1)*(4*x-1)*(4*x+1)). (End) a(n) = floor(28*4^n/15) for even n>=0; a(n) = floor(27*4^n/15) for odd n. - Karl V. Keller, Jr., Oct 09 2020 EXAMPLE 1; 1, 1, 1; 1, 1, 1, 0, 1; 1, 1, 1, 0, 0, 1, 1; 1, 1, 1, 0, 1, 1, 1, 0, 1; ... From Michael De Vlieger, Oct 08 2015: (Start) First 8 rows, representing ON cells as "1", OFF cells within the bounds of ON cells as "0", interpreted as a binary number at left, the decimal equivalent appearing at right: 1 = 1 111 = 7 1 1101 = 29 111 0011 = 115 1 1101 1101 = 477 111 0011 0011 = 1843 1 1101 1101 1101 = 7645 111 0011 0011 0011 = 29491 11101 1101 1101 1101 = 122333 (End) MATHEMATICA Table[(-16 + (-4)^n - 10 (-1)^n + 55*4^n)/30, {n, 0, 24}] (* or *) clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; FromDigits[#, 2] & /@ Map[clip, CellularAutomaton[158, {{1}, 0}, 24]] (* Michael De Vlieger, Oct 08 2015 *) PROG (PARI) Vec(-(4*x^3-12*x^2-7*x-1)/((x-1)*(x+1)*(4*x-1)*(4*x+1)) + O(x^30)) \\ Colin Barker, Oct 08 2015 (PARI) vector(100, n, n--; (1/30)*(-16+(-4)^n-10*(-1)^n+55*4^n)) \\ Altug Alkan, Oct 08 2015 (Python) print([27*4**n//15 if n%2 else 28*4**n//15 for n in range(50)]) # Karl V. Keller, Jr., May 07 2022 CROSSREFS Cf. A071037 (cells), A265379 (binary). Sequence in context: A124828 A296646 A037094 * A072261 A066744 A037576 Adjacent sequences: A118168 A118169 A118170 * A118172 A118173 A118174 KEYWORD nonn,base,easy AUTHOR Eric W. Weisstein, Apr 13 2006 STATUS approved

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

Last modified September 16 13:56 EDT 2024. Contains 375976 sequences. (Running on oeis4.)