A250393 Number of length 7+3 0..n arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms.

6, 1816, 74528, 1162292, 10203222, 61304844, 281731072, 1060924200, 3426341574, 9795159264, 25359512992, 60478538588, 134596669142, 282388072596, 563045400576, 1073890795600, 1969791998214, 3490220036904, 5996191000608

Offset

1,1

Comments

Row 7 of A250387.

Links

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

Formula

Empirical: a(n) = n^10 - (2/3)*n^9 + (4087/840)*n^8 - (259/90)*n^7 + (713/180)*n^6 + (119/90)*n^5 - (1493/360)*n^4 + (202/45)*n^3 - (844/315)*n^2 + (11/15)*n.

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

G.f.: 2*x*(3 + 875*x + 27441*x^2 + 220687*x^3 + 609695*x^4 + 647425*x^5 + 267419*x^6 + 39317*x^7 + 1538*x^8) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)

Example

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

Crossrefs

Sequence in context: A330056 A258900 A357760 * A221627 A160301 A209496

Adjacent sequences: A250390 A250391 A250392 * A250394 A250395 A250396

Keyword

nonn

Author

R. H. Hardin, Nov 20 2014

Status

approved