A241968 Number of length 5+3 0..n arrays with no consecutive four elements summing to more than 2*n.

97, 1895, 16649, 92037, 376559, 1247602, 3536286, 8889273, 20314789, 42967177, 85231367, 160175717, 287448747, 495702356, 825631180, 1333724817, 2096836713, 3217680571, 4831372213, 7113141893, 10287349127, 14637939174, 20520487370

Offset: 1

Author

R. H. Hardin, May 03 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 5 of A241964.

Formula

Empirical: a(n) = (589/3360)*n^8 + (349/210)*n^7 + (2483/360)*n^6 + (1317/80)*n^5 + (35819/1440)*n^4 + (1963/80)*n^3 + (19597/1260)*n^2 + (613/105)*n + 1.

Conjectures from Colin Barker, Oct 31 2018: (Start)

G.f.: x*(97 + 1022*x + 3086*x^2 + 2268*x^3 + 632*x^4 - 65*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)