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

1,1

Links

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

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

Example

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

Crossrefs

Column 3 of A241619.

Sequence in context: A231293 A227771 A228023 * A331753 A345124 A049390

Adjacent sequences: A241606 A241607 A241608 * A241610 A241611 A241612

Keyword

nonn

Author

R. H. Hardin, Apr 26 2014

Status

approved