A221568 Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1.

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

Author

R. H. Hardin, Jan 20 2013

Keywords

• nonn
• easy

Comments

Column 3 of A221573.

Examples

			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
		

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).

Programs

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

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