A241620 Number of length 5+2 0..n arrays with no consecutive three elements summing to more than n.

19, 147, 711, 2567, 7586, 19374, 44274, 92697, 180829, 332761, 583089, 980031, 1589108, 2497436, 3818676, 5698689, 8321943, 11918719, 16773163, 23232231, 31715574, 42726410, 56863430, 74833785, 97467201, 125731269, 160747957

Offset: 1

Author

R. H. Hardin, Apr 26 2014

Keywords

• nonn

Examples

			Some solutions for n=5:
..3....3....1....0....2....2....2....3....0....0....0....2....1....5....0....0
..2....2....3....3....2....0....1....2....3....3....5....0....1....0....1....0
..0....0....1....0....1....3....0....0....1....0....0....2....3....0....1....2
..0....0....1....0....1....1....2....1....1....0....0....1....0....0....1....2
..2....1....0....3....0....1....1....3....1....0....4....0....1....0....1....1
..0....3....0....0....0....1....0....0....2....2....1....2....1....2....1....0
..3....0....3....1....1....0....2....2....2....1....0....3....0....2....3....3
		

Links

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

Crossrefs

Row 5 of A241619.

Formula

Empirical: a(n) = (47/5040)*n^7 + (47/360)*n^6 + (7/9)*n^5 + (23/9)*n^4 + (3599/720)*n^3 + (2093/360)*n^2 + (26/7)*n + 1.

Conjectures from Colin Barker, Oct 30 2018: (Start)

G.f.: x*(19 - 5*x + 67*x^2 - 69*x^3 + 56*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)