A268255 Number of length-(n+1) 0..2 arrays with new repeated values introduced in sequential order starting with zero.

7, 17, 42, 106, 273, 717, 1918, 5218, 14413, 40349, 114282, 326938, 943257, 2740797, 8010982, 23529346, 69385813, 205282157, 608959218, 1810358938, 5391414273, 16078923309, 48007516942, 143470822498, 429083952157, 1284051486077

Offset: 1

Author

R. H. Hardin, Jan 29 2016

Keywords

• nonn

Examples

			Some solutions for n=8:
..0....1....1....0....0....1....0....0....2....1....0....1....2....0....0....1
..0....0....0....0....0....0....0....2....0....2....1....2....1....1....0....0
..2....0....0....2....0....1....1....0....0....0....2....1....2....0....1....2
..0....1....0....0....2....0....0....0....0....0....1....2....1....0....0....0
..1....1....1....1....0....2....0....0....1....2....2....0....0....2....0....2
..0....1....2....1....2....0....1....1....1....1....1....0....1....1....1....1
..1....1....1....0....0....0....0....0....1....0....2....1....0....0....1....0
..0....1....2....1....2....2....2....0....2....1....0....0....0....1....1....0
..2....1....0....0....1....1....1....1....2....0....0....2....1....1....1....1
		

Links

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

Crossrefs

Column 2 of A268261.

Formula

Empirical: a(n) = 7*a(n-1) - 15*a(n-2) + 7*a(n-3) + 6*a(n-4).

Conjectures from Colin Barker, Jan 11 2019: (Start)

G.f.: x*(7 - 32*x + 28*x^2 + 18*x^3) / ((1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)).

a(n) = 2^n + 3^n/2 + (3/4-1/sqrt(2))*(1-sqrt(2))^n + (3/4+1/sqrt(2))*(1+sqrt(2))^n.

(End)