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 A084509 Number of ground-state 3-ball juggling sequences of period n. 10
 1, 1, 2, 6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184, 1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624, 105553116266496, 422212465065984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence counts the length n asynchronic site swaps given in A084501/A084502. Equals row sums of triangle A145463. - Gary W. Adamson, Oct 11 2008 a(n) is the number of permutations of length n+1 avoiding the partially ordered pattern (POP) {1>2, 1>3, 1>4, 1>5} of length 5. That is, the number of length n+1 permutations having no subsequences of length 5 in which the first element is the largest. - Sergey Kitaev, Dec 11 2020 a(n) is the number of permutations p[1]..p[n] of {1,...,n} with p[j+1] < p[j]+4 for 0 < j < n. - Don Knuth, Apr 25 2022 REFERENCES B. Polster, The Mathematics of Juggling, Springer-Verlag, 2003, p. 48. LINKS Michael De Vlieger, Table of n, a(n) for n = 0..1662 Fan Chung and R. L. Graham, Primitive juggling sequences, Amer. Math. Monthly 115(3) (2008), 185-19. Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019. Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26. Kai Ting Keshia Yap, David Wehlau, and Imed Zaguia, Permutations Avoiding Certain Partially-ordered Patterns, arXiv:2101.12061 [math.CO], 2021. Index entries for linear recurrences with constant coefficients, signature (4). FORMULA a(n) = n! for n <= 4, a(n) = 6*4^(n-3) = A002023(n-3) for n >= 3. G.f.: 1 + x*(1 - 2*x - 2*x^2)/(1 - 4*x). - Philippe Deléham, Aug 16 2005 MAPLE A084509 := n -> `if`((n<4), n!, 6*(4^(n-3))); INVERT([seq(A084519(n), n=1..12)]); MATHEMATICA LinearRecurrence[{4}, {1, 2, 6}, 30] (* Harvey P. Dale, Aug 23 2018 *) CROSSREFS First differences of A084508. INVERT transform of A084519. Cf. A002023, A084501, A084502, A084529, A145463. Sequence in context: A179350 A179356 A179363 * A334767 A323260 A147915 Adjacent sequences: A084506 A084507 A084508 * A084510 A084511 A084512 KEYWORD nonn,easy AUTHOR Antti Karttunen, Jun 02 2003 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Dec 11 2020 STATUS approved

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Last modified December 4 04:59 EST 2022. Contains 358544 sequences. (Running on oeis4.)