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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A118173 Decimal representation of n-th iteration of the Rule 188 elementary cellular automaton starting with a single black cell. 5
1, 3, 5, 15, 29, 55, 93, 247, 477, 887, 1501, 3959, 7645, 14199, 24029, 63351, 122333, 227191, 384477, 1013623, 1957341, 3635063, 6151645, 16217975, 31317469, 58161015, 98426333, 259487607, 501079517, 930576247, 1574821341, 4151801719, 8017272285 (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 188

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for linear recurrences with constant coefficients, signature (0,1,0,16,0,-16).

Index entries for sequences related to cellular automata

FORMULA

a(n) = (1/30)*(-14 + 3*i*(2*i)^n + 55*2^n) for n odd,

a(n) = (1/15)*(-13 + 3*(2*i)^n + 25*2^n) for n even, where i = sqrt(-1).

From Colin Barker, Oct 08 2015: (Start)

G.f.: -(8*x^5-8*x^4-12*x^3-4*x^2-3*x-1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)*(4*x^2+1)).

a(n) = a(n-2) + 16*a(n-4) - 16*a(n-6) for n>5. (End)

E.g.f.: (1/15)*(6*sinh(x) + (5/2)*sinh(2x) + 25*exp(2x) - 13*exp(x)) + (1/10)*(2*cos(2x)-sin(2x)). - G. C. Greubel, Oct 08 2015

a(n) = floor(28*4^n/15) + 2^n - floor(28*2^n/15)*2^n. - Karl V. Keller, Jr., Nov 11 2021

EXAMPLE

1; --> 1

0, 1, 1; --> 3

0, 0, 1, 0, 1; --> 5

0, 0, 0, 1, 1, 1, 1; --> 15

0, 0, 0, 0, 1, 1, 1, 0, 1; --> 29

MATHEMATICA

clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; FromDigits[#, 2] & /@ Map[clip, CellularAutomaton[188, {{1}, 0}, 32]] (* Michael De Vlieger, Oct 08 2015 *)

RecurrenceTable[{a[n+6]==a[n+4] + 16*a[n+2] - 16*a[n], a[0]==1, a[1]==3, a[2]==5, a[3]==15, a[4]==29, a[5]==55}, a, {n, 0, 100}] (* _G. C. Greubel, Oct 08 2015 *)

PROG

(PARI) Vec(-(8*x^5-8*x^4-12*x^3-4*x^2-3*x-1)/((x-1)*(x+1)*(2*x-1)*(2*x+1)*(4*x^2+1)) + O(x^40)) \\ Colin Barker, Oct 08 2015

(Python) print([28*4**n//15 + 2**n - (28*2**n//15)*2**n for n in range(50)]) # Karl V. Keller, Jr., Nov 11 2021

CROSSREFS

Cf. A118174, A265427.

Sequence in context: A340670 A284031 A284410 * A079450 A284482 A166956

Adjacent sequences: A118170 A118171 A118172 * A118174 A118175 A118176

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 13:46 EST 2022. Contains 358700 sequences. (Running on oeis4.)