A241622 Number of length 7+2 0..n arrays with no consecutive three elements summing to more than n.

41, 556, 4175, 21631, 86828, 289248, 835812, 2159025, 5093737, 11151140, 22925695, 44678543, 83149600, 148659968, 256576512, 429221457, 698321649, 1108104700, 1719162599, 2613217519, 3898939484, 5718981280, 8258412500, 11754751905

Offset

1,1

Links

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

Formula

Empirical: a(n) = (131/60480)*n^9 + (131/3360)*n^8 + (3137/10080)*n^7 + (347/240)*n^6 + (12407/2880)*n^5 + (4097/480)*n^4 + (169957/15120)*n^3 + (7963/840)*n^2 + (487/105)*n + 1.

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

G.f.: x*(41 + 146*x + 460*x^2 - 19*x^3 + 283*x^4 - 209*x^5 + 120*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

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

Crossrefs

Row 7 of A241619.

Sequence in context: A208048 A298839 A301399 * A276251 A298627 A078947

Adjacent sequences: A241619 A241620 A241621 * A241623 A241624 A241625

Keyword

nonn

Author

R. H. Hardin, Apr 26 2014

Status

approved