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A200835
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Number of 0..5 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.
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1
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176, 846, 4108, 19930, 96690, 469116, 2276028, 11042700, 53576350, 259938722, 1261156090, 6118806300, 29686880836, 144033141554, 698811908924, 3390456382404, 16449625906804, 79809371351400, 387214626739458
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OFFSET
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1,1
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COMMENTS
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Column 5 of A200838.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = 6*a(n-1) -6*a(n-2) +3*a(n-3) -5*a(n-4) +3*a(n-5) -2*a(n-6) +a(n-7).
Empirical g.f.: 2*x*(88 - 105*x + 44*x^2 - 85*x^3 + 50*x^4 - 33*x^5 + 18*x^6) / (1 - 6*x + 6*x^2 - 3*x^3 + 5*x^4 - 3*x^5 + 2*x^6 - x^7). - Colin Barker, Oct 14 2017
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EXAMPLE
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Some solutions for n=3
..3....5....0....4....2....3....2....5....3....1....2....0....0....4....1....3
..3....4....3....1....1....5....0....1....0....1....3....5....2....5....4....4
..0....4....0....1....5....3....4....2....5....1....3....4....1....0....4....0
..0....0....2....4....0....3....2....2....4....3....1....5....1....4....4....0
..1....1....1....2....0....5....3....2....4....3....1....5....2....0....0....5
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CROSSREFS
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Sequence in context: A336026 A063344 A075291 * A133063 A264892 A223611
Adjacent sequences: A200832 A200833 A200834 * A200836 A200837 A200838
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin Nov 23 2011
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STATUS
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approved
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