A241621 Number of length 6+2 0..n arrays with no consecutive three elements summing to more than n.

28, 287, 1730, 7483, 25774, 75180, 193194, 449295, 963886, 1934647, 3672032, 6645821, 11544820, 19351984, 31437420, 49671909, 76563768, 115422055, 170549302, 247467143, 353178386, 496469260, 688255750, 941978115, 1274047866

Offset

1,1

Links

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

Formula

Empirical: a(n) = (13/2880)*n^8 + (13/180)*n^7 + (145/288)*n^6 + (719/360)*n^5 + (14197/2880)*n^4 + (2789/360)*n^3 + (121/16)*n^2 + (251/60)*n + 1.

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

G.f.: x*(28 + 35*x + 155*x^2 - 107*x^3 + 127*x^4 - 84*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

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

Crossrefs

Row 6 of A241619.

Sequence in context: A250649 A107418 A183484 * A027781 A219626 A126662

Adjacent sequences: A241618 A241619 A241620 * A241622 A241623 A241624

Keyword

nonn

Author

R. H. Hardin, Apr 26 2014

Status

approved