A249967 Number of length 7+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, 8823, 709814, 18707320, 251002319, 2149795141, 13385651492, 65717571120, 268511791119, 948021599547, 2972106528666, 8443442678840, 22076610372895, 53774915777897, 123215084622184, 267660712891040, 554792683762767

Offset

1,1

Comments

Row 7 of A249960.

Links

R. H. Hardin, Table of n, a(n) for n = 1..42

Formula

Empirical: a(n) = n^12 - (53/42)*n^11 + (1404/175)*n^10 - (8593/1260)*n^9 + (8647/1260)*n^8 + (3511/252)*n^7 - (43133/1800)*n^6 + (41323/2520)*n^5 + (21641/2520)*n^4 - (2225/168)*n^3 + (7339/1050)*n^2 - (158/105)*n.

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

G.f.: x*(15 + 8628*x + 596285*x^2 + 10163642*x^3 + 60659998*x^4 + 149218290*x^5 + 162389570*x^6 + 78777198*x^7 + 16029715*x^8 + 1141682*x^9 + 16577*x^10) / (1 - x)^13.

a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.

(End)

Example

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

Crossrefs

Sequence in context: A074488 A059950 A198979 * A308156 A304397 A206593

Adjacent sequences: A249964 A249965 A249966 * A249968 A249969 A249970

Keyword

nonn

Author

R. H. Hardin, Nov 09 2014

Status

approved