A249848 Number of length 4+4 0..n arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms.

10, 653, 11052, 92190, 499654, 2029683, 6712760, 19039308, 47942370, 109802473, 232780196, 462822282, 871727454, 1567698415, 2708846832, 4520158424, 7314465594, 11518015365, 17701260700, 26615543606, 39236378742, 56814086571

Offset

1,1

Comments

Row 4 of A249844.

Links

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

Formula

Empirical: a(n) = n^8 + (13/21)*n^7 + (101/30)*n^6 + (71/30)*n^5 + (2/3)*n^4 + 2*n^3 - (1/30)*n^2 + (1/70)*n.

Conjectures from Colin Barker, Aug 18 2017: (Start)

G.f.: x*(10 + 563*x + 5535*x^2 + 15390*x^3 + 14224*x^4 + 4287*x^5 + 311*x^6) / (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
..0....2....0....4....3....3....2....0....3....2....3....4....0....0....2....4
..4....4....2....4....0....1....0....4....0....0....1....1....3....4....4....1
..1....4....2....4....3....3....1....1....2....4....3....0....2....3....3....4
..0....4....0....3....4....0....0....3....4....0....0....0....0....0....0....4
..3....2....1....0....2....3....3....2....0....3....0....3....1....2....1....2
..2....1....4....1....0....2....1....0....4....3....4....2....0....0....0....1
..0....0....2....0....1....0....0....0....3....2....1....4....3....4....1....1
..2....4....2....3....3....1....1....2....2....1....2....3....2....2....4....4

Crossrefs

Sequence in context: A280897 A099024 A126680 * A214108 A174061 A058174

Adjacent sequences: A249845 A249846 A249847 * A249849 A249850 A249851

Keyword

nonn

Author

R. H. Hardin, Nov 07 2014

Status

approved