OFFSET
1,2
COMMENTS
Column 3 of A221573.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
Sergey Kitaev, Jeffrey Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.
Index entries for linear recurrences with constant coefficients, signature (3,2,-1,1).
FORMULA
a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4).
G.f.: 2*x^2*(5 - 2*x + x^2) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - Colin Barker, Jan 31 2017
EXAMPLE
Some solutions for n=6
..1....0....1....0....3....0....3....2....0....0....3....0....0....0....2....0
..3....2....1....2....1....2....3....0....2....2....1....0....0....3....2....0
..2....2....1....3....0....0....0....3....3....3....2....0....0....2....0....0
..2....2....1....3....3....1....3....3....0....0....0....3....3....2....1....2
..3....3....1....3....1....3....3....2....0....1....1....0....3....0....1....2
..0....0....1....3....1....3....3....2....2....1....1....3....3....0....3....2
PROG
(PARI) concat(0, Vec(2*x^2*(5 - 2*x + x^2) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)) + O(x^30))) \\ Colin Barker, Jan 31 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Jan 20 2013
STATUS
approved