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A255625
Number of length n+3 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.
1
81, 243, 729, 2040, 5088, 11386, 23298, 44361, 79692, 136494, 224676, 357603, 552993, 833979, 1230355, 1780026, 2530683, 3541725, 4886451, 6654546, 8954886, 11918688, 15703032, 20494783, 26514942, 34023456, 43324518, 54772389, 68777775
OFFSET
1,1
COMMENTS
Row 3 of A255622.
LINKS
FORMULA
Empirical: a(n) = (1/40320)*n^8 + (1/672)*n^7 + (29/960)*n^6 + (39/80)*n^5 + (2463/640)*n^4 + (1/32)*n^3 + (112103/10080)*n^2 + (44923/840)*n + 12.
Empirical g.f.: x*(81 - 486*x + 1458*x^2 - 2577*x^3 + 2766*x^4 - 1790*x^5 + 672*x^6 - 135*x^7 + 12*x^8) / (1 - x)^9. - Colin Barker, Jan 21 2018
EXAMPLE
Some solutions for n=4:
..2....1....0....0....2....1....1....2....0....0....0....0....1....2....2....0
..1....2....2....0....0....2....2....1....1....0....2....0....1....0....2....1
..1....0....2....2....0....2....0....2....0....0....0....2....1....1....1....2
..0....2....2....1....1....0....0....0....0....0....2....1....1....0....0....0
..2....0....1....2....0....2....1....2....2....0....1....1....0....0....2....1
..2....0....2....1....2....0....1....0....2....1....1....1....2....2....2....1
..0....1....0....2....1....0....1....2....1....1....0....2....0....2....2....0
CROSSREFS
Cf. A255622.
Sequence in context: A211690 A205055 A335843 * A205048 A008876 A031456
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 28 2015
STATUS
approved