

A255624


Number of length n+2 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.


1



27, 81, 243, 694, 1803, 4248, 9186, 18483, 35016, 63060, 108774, 180801, 290998, 455313, 694827, 1036980, 1517001, 2179563, 3080685, 4289904, 5892741, 7993486, 10718328, 14218857, 18675966, 24304182, 31356456, 40129443, 50969304, 64278063
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Row 2 of A255622.


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210


FORMULA

Empirical: a(n) = (1/40320)*n^8 + (13/10080)*n^7 + (59/2880)*n^6 + (61/360)*n^5 + (5167/5760)*n^4 + (901/1440)*n^3 + (17077/3360)*n^2 + (3977/280)*n + 6.
Empirical g.f.: x*(3  2*x)*(9  48*x + 130*x^2  195*x^3 + 171*x^4  87*x^5 + 24*x^6  3*x^7) / (1  x)^9.  Colin Barker, Jan 21 2018


EXAMPLE

Some solutions for n=4:
..0....0....2....2....0....2....1....0....2....2....2....0....0....1....1....0
..0....2....0....0....2....0....1....2....0....1....1....1....0....1....2....1
..1....2....2....2....1....2....2....1....0....0....0....2....1....2....0....0
..1....1....1....2....2....2....2....0....2....0....0....0....2....1....2....2
..2....0....1....0....2....2....2....0....1....1....2....0....1....2....2....2
..2....1....2....2....2....1....0....0....2....0....1....2....1....0....0....1


CROSSREFS

Cf. A255622.
Sequence in context: A216438 A292872 A057609 * A008884 A031455 A045004
Adjacent sequences: A255621 A255622 A255623 * A255625 A255626 A255627


KEYWORD

nonn


AUTHOR

R. H. Hardin, Feb 28 2015


STATUS

approved



