A241609 Number of length n+2 0..3 arrays with no consecutive three elements summing to more than 3.

20, 50, 125, 295, 711, 1730, 4175, 10077, 24377, 58928, 142396, 344201, 832011, 2010980, 4860690, 11748840, 28397936, 68640170, 165909570, 401018224, 969296175, 2342874854, 5662936565, 13687818660, 33084669767, 79968578621

Offset: 1

Author

R. H. Hardin, Apr 26 2014

Keywords

• nonn

Examples

			Some solutions for n=5:
..1....2....3....2....1....0....3....0....1....1....1....1....1....3....2....0
..0....1....0....1....2....1....0....0....1....1....0....1....1....0....0....1
..1....0....0....0....0....2....0....0....0....0....1....0....1....0....0....1
..0....0....1....0....0....0....1....0....1....2....2....0....1....2....3....1
..0....0....2....1....1....1....1....0....1....1....0....1....0....1....0....0
..0....2....0....2....2....1....1....0....0....0....0....0....1....0....0....0
..3....1....1....0....0....1....0....1....1....2....0....0....1....2....1....3
		

Links

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

Crossrefs

Column 3 of A241619.

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-3) - 3*a(n-4) - a(n-5) - 3*a(n-6) + 2*a(n-7) + a(n-9) - a(n-10).

Empirical g.f.: x*(20 + 10*x + 25*x^2 - 35*x^3 - 19*x^4 - 22*x^5 + 20*x^6 + 3*x^7 + 6*x^8 - 10*x^9) / ((1 - x)*(1 - x - x^2 - 5*x^3 - 2*x^4 - x^5 + 2*x^6 - x^9)). - Colin Barker, Oct 30 2018