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 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). 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

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