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 A255047 1 together with the positive terms of A000225. 11
 1, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also, right border of A246674 arranged as an irregular triangle. Essentially the same as A168604, A126646 and A000225. Total number of lambda-parking functions induced by all partitions of n. a(0)=1: [], a(1)=1: , a(2)=3: , , [1,1], a(4)=7: , , , [1,1], [1,2], [2,1], [1,1,1]. - Alois P. Heinz, Dec 04 2015 Also, the decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 645", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 19 2017 Also number of multiset partitions of {1,1} U [n] into exactly 2 nonempty parts. a(2) = 3: 111|2, 11|12, 1|112. - Alois P. Heinz, Aug 18 2017 Also, the number of unlabeled connected P-series (equivalently, connected P-graphs) with n+1 elements. - Salah Uddin Mohammad, Nov 19 2021 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015. R. Stanley, Parking Functions, 2011. Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science Wolfram Research, Wolfram Atlas of Simple Programs Index entries for sequences related to cellular automata Index to 2D 5-Neighbor Cellular Automata Index to Elementary Cellular Automata Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA From Alois P. Heinz, Feb 19 2015: (Start) O.g.f.: (1 -2*x +2*x^2)/((1-x)*(1-2*x)). E.g.f.: exp(2*x) - exp(x) + 1. (End) a(n) = A078485(n+1) for n > 2. - Georg Fischer, Oct 22 2018 MATHEMATICA CoefficientList[Series[(1 -2*x +2*x^2)/((1-x)*(1-2*x)), {x, 0, 33}], x] (* or *) LinearRecurrence[{3, -2}, {1, 1, 3}, 40] (* Vincenzo Librandi, Jul 20 2017 *) Table[2^n -1 +Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Feb 07 2021 *) PROG (Sage) +[2^n -1 for n in (1..40)] # G. C. Greubel, Feb 07 2021 (Magma)  cat [2^n -1: n in [1..40]]; // G. C. Greubel, Feb 07 2021 (Python) def A255047(n): return -1^(-1<

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Last modified May 28 09:20 EDT 2023. Contains 362999 sequences. (Running on oeis4.)