A249963 Number of length 3+5 0..n arrays with no six consecutive terms having the maximum of any two terms equal to the minimum of the remaining four terms.

15, 897, 14094, 111746, 585069, 2319123, 7532380, 21069828, 52478667, 119135973, 250738026, 495501318, 928465577, 1662329463, 2861289912, 4758396424, 7676971911, 12056692041, 18484955334, 27734216586, 40805996517, 58982320859

Offset

1,1

Comments

Row 3 of A249960.

Links

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

Formula

Empirical: a(n) = n^8 + (152/105)*n^7 + (62/15)*n^6 + (26/5)*n^5 + (1/2)*n^4 + (19/15)*n^3 + (28/15)*n^2 - (29/70)*n.

Conjectures from Colin Barker, Aug 21 2017: (Start)

G.f.: x*(15 + 762*x + 6561*x^2 + 15932*x^3 + 13281*x^4 + 3594*x^5 + 175*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:
..4....1....4....0....1....4....3....3....1....3....3....0....2....2....0....1
..4....1....3....2....3....1....2....4....4....1....2....2....2....0....2....1
..0....0....0....3....0....0....3....0....0....2....0....4....3....0....2....0
..0....1....0....3....2....4....3....0....0....0....3....0....3....4....0....3
..4....2....4....1....1....0....0....2....3....1....1....1....3....4....4....0
..2....0....1....3....0....1....4....3....1....0....0....3....3....4....4....3
..4....2....3....1....1....2....0....4....1....3....4....4....0....4....1....4
..1....1....4....2....2....3....3....3....1....1....2....4....2....3....0....4

Crossrefs

Sequence in context: A232364 A264562 A211109 * A157462 A268166 A042747

Adjacent sequences: A249960 A249961 A249962 * A249964 A249965 A249966

Keyword

nonn

Author

R. H. Hardin, Nov 09 2014

Status

approved