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

Author

R. H. Hardin, Apr 26 2014

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 7 of A241619.

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)