A241937 Number of length 1+4 0..n arrays with no consecutive five elements summing to more than 2*n.

16, 96, 357, 1007, 2373, 4928, 9318, 16389, 27214, 43120, 65715, 96915, 138971, 194496, 266492, 358377, 474012, 617728, 794353, 1009239, 1268289, 1577984, 1945410, 2378285, 2884986, 3474576, 4156831, 4942267, 5842167, 6868608, 8034488

Offset

1,1

Links

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

Formula

Empirical: a(n) = (9/40)*n^5 + (19/12)*n^4 + (101/24)*n^3 + (65/12)*n^2 + (107/30)*n + 1.

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

G.f.: x*(16 + 21*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Row 1 of A241936.

Sequence in context: A192037 A143060 A006637 * A014344 A239613 A100313

Adjacent sequences: A241934 A241935 A241936 * A241938 A241939 A241940

Keyword

nonn

Author

R. H. Hardin, May 02 2014

Status

approved