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 A094286 Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 1, s(n) = 1. 1
 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2187, 5787, 15435, 41419, 111659, 302059, 819243, 2226219, 6058155, 16503211, 44991659, 122727595, 334914219, 914235051, 2496201387, 6816678571, 18617371307, 50851322539, 138903833259, 379443202731, 1036559854251 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the number of Motzkin n-paths of height <= 4. - Alois P. Heinz, Nov 24 2023 LINKS Table of n, a(n) for n=0..30. S. Felsner and D. Heldt, Lattice Path Enumeration and Toeplitz Matrices, J. Int. Seq. 18 (2015) # 15.1.3. Daniel Heldt, On the mixing time of the face flip-and up/down Markov chain for some families of graphs, Dissertation, Mathematik und Naturwissenschaften der Technischen Universitat Berlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften, 2016. Index entries for linear recurrences with constant coefficients, signature (5,-6,-2,4). FORMULA a(n) = (1/12)*(4 + 3*2^n + (1-sqrt(3))^n + (1+sqrt(3))^n). a(n) = 1/3 + 2^(n-2) + A026150(n)/6. G.f.: -x*(1-3*x+3*x^3) / ( (x-1)*(2*x-1)*(2*x^2+2*x-1) ). - R. J. Mathar, Dec 20 2011 MATHEMATICA LinearRecurrence[{5, -6, -2, 4}, {1, 2, 4, 9}, 30] (* Harvey P. Dale, Feb 01 2012 *) CROSSREFS Cf. A001006. Sequence in context: A005207 A257519 A257387 * A094287 A094288 A168051 Adjacent sequences: A094283 A094284 A094285 * A094287 A094288 A094289 KEYWORD easy,nonn AUTHOR Herbert Kociemba, Jun 02 2004 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Nov 24 2023 STATUS approved

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Last modified May 22 06:24 EDT 2024. Contains 372743 sequences. (Running on oeis4.)