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A221568
Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1.
2
0, 10, 26, 100, 342, 1210, 4240, 14898, 52306, 183684, 645006, 2264978, 7953568, 27929338, 98075178, 344395620, 1209361446, 4246729738, 14912591664, 52366268642, 183886620962, 645726538244, 2267499179678, 7962430263202, 27960449231680, 98184435580010
OFFSET
1,2
COMMENTS
Column 3 of A221573.
LINKS
Sergey Kitaev, Jeffrey Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.
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
Sequence in context: A220155 A321311 A051966 * A092774 A259979 A368503
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Jan 20 2013
STATUS
approved