login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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