A241940 Number of length 4+4 0..n arrays with no consecutive five elements summing to more than 2*n.

71, 1187, 9500, 49355, 193179, 619132, 1710198, 4211175, 9462805, 19735067, 38684438, 71962709, 128007725, 219049200, 362365540, 581830389, 909790395, 1389318475, 2076889640, 3045529223, 4388486135, 6223486556, 8697626250

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1391/20160)*n^8 + (197/252)*n^7 + (1819/480)*n^6 + (3719/360)*n^5 + (5593/320)*n^4 + (1369/72)*n^3 + (66343/5040)*n^2 + (2257/420)*n + 1.

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

G.f.: x*(71 + 548*x + 1373*x^2 + 623*x^3 + 222*x^4 - 83*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)

Example

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

Crossrefs

Row 4 of A241936.

Sequence in context: A071827 A289899 A267475 * A254872 A198449 A093271

Adjacent sequences: A241937 A241938 A241939 * A241941 A241942 A241943

Keyword

nonn

Author

R. H. Hardin, May 02 2014

Status

approved