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 A200786 Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases. 1
 16, 75, 225, 530, 1071, 1946, 3270, 5175, 7810, 11341, 15951, 21840, 29225, 38340, 49436, 62781, 78660, 97375, 119245, 144606, 173811, 207230, 245250, 288275, 336726, 391041, 451675, 519100, 593805, 676296, 767096, 866745, 975800, 1094835 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 2 of A200785. LINKS R. H. Hardin, Table of n, a(n) for n = 1..140 A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, Annals. Combin., 7 (2003), 1-14. See Th. 3.13. FORMULA Empirical: a(n) = (17/24)*n^4 + (43/12)*n^3 + (151/24)*n^2 + (53/12)*n + 1. Conjectures from Colin Barker, Oct 15 2017: (Start) G.f.: x*(16 - 5*x + 10*x^2 - 5*x^3 + x^4) / (1 - x)^5. a(n) = (24 + 106*n + 151*n^2 + 86*n^3 + 17*n^4) / 24. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5. (End) EXAMPLE Some solutions for n=3 ..0....1....0....3....2....3....3....2....3....1....0....1....0....3....1....0 ..0....3....3....1....2....3....2....0....3....3....3....2....0....2....1....2 ..3....2....3....1....1....0....2....3....3....1....1....1....2....1....3....1 ..1....2....1....2....3....0....1....0....3....2....2....2....2....2....1....1 CROSSREFS Sequence in context: A126403 A197873 A232863 * A250353 A212690 A244835 Adjacent sequences: A200783 A200784 A200785 * A200787 A200788 A200789 KEYWORD nonn AUTHOR R. H. Hardin, Nov 22 2011 STATUS approved

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Last modified December 2 23:17 EST 2023. Contains 367526 sequences. (Running on oeis4.)