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

1,1

Links

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

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)

Example

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

Crossrefs

Row 5 of A241619.

Sequence in context: A264679 A200530 A183748 * A069423 A183740 A162872

Adjacent sequences: A241617 A241618 A241619 * A241621 A241622 A241623

Keyword

nonn

Author

R. H. Hardin, Apr 26 2014

Status

approved