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 A200787 Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases. 1
 32, 216, 840, 2425, 5796, 12152, 23136, 40905, 68200, 108416, 165672, 244881, 351820, 493200, 676736, 911217, 1206576, 1573960, 2025800, 2575881, 3239412, 4033096, 4975200, 6085625, 7385976, 8899632, 10651816, 12669665, 14982300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 3 of A200785. LINKS R. H. Hardin, Table of n, a(n) for n = 1..139 FORMULA Empirical: a(n) = (7/12)*n^5 + (47/12)*n^4 + (39/4)*n^3 + (133/12)*n^2 + (17/3)*n + 1. Conjectures from Colin Barker, Oct 15 2017: (Start) G.f.: x*(32 + 24*x + 24*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6. a(n) = (1 + n)^2*(12 + 44*n + 33*n^2 + 7*n^3) / 12 . a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6. (End) EXAMPLE Some solutions for n=3 ..2....1....3....2....2....3....1....3....1....1....2....1....0....1....2....0 ..0....0....3....3....1....2....3....1....3....2....0....0....3....3....2....0 ..0....1....1....3....3....1....3....1....0....0....0....2....3....2....3....0 ..3....1....1....1....1....0....3....2....3....3....3....2....1....1....0....0 ..0....1....1....0....2....3....3....1....1....0....1....0....3....1....2....3 CROSSREFS Sequence in context: A125342 A126500 A160538 * A250354 A146089 A250232 Adjacent sequences: A200784 A200785 A200786 * A200788 A200789 A200790 KEYWORD nonn AUTHOR R. H. Hardin, Nov 22 2011 STATUS approved

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Last modified September 26 19:26 EDT 2023. Contains 365666 sequences. (Running on oeis4.)