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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
OFFSET
1,1
COMMENTS
Row 2 of A200785.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 22 2011
STATUS
approved