A241967 Number of length 4+3 0..n arrays with no consecutive four elements summing to more than 2*n.

57, 775, 5211, 23320, 80132, 228826, 569874, 1277427, 2634115, 5075433, 9244885, 16061058, 26797798, 43178660, 67486804, 102691509, 152592477, 221983099, 316833855, 444497020, 613933848, 835965406, 1123548230, 1492075975

Offset: 1

Author

R. H. Hardin, May 03 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 4 of A241964.

Formula

Empirical: a(n) = (293/1260)*n^7 + (691/360)*n^6 + (2443/360)*n^5 + (121/9)*n^4 + (5857/360)*n^3 + (4369/360)*n^2 + (2189/420)*n + 1.

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

G.f.: x*(57 + 319*x + 607*x^2 + 140*x^3 + 70*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)