A250340 Number of length 4+5 0..n arrays with every six consecutive terms having the maximum of some three terms equal to the minimum of the remaining three terms.

172, 4409, 37824, 193437, 725596, 2210213, 5794496, 13561449, 29037004, 57870241, 108719744, 194381733, 333198204, 550785901, 882129536, 1374085265, 2088343020, 3104898889, 4526091328, 6481257581, 9132069276, 12678608757, 17366250304

Offset

1,1

Links

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

Formula

Empirical: a(n) = (9/140)*n^8 + (27/10)*n^7 + 19*n^6 + 48*n^5 + (1203/20)*n^4 + (1189/30)*n^3 + (81/14)*n^2 - (13/3)*n + 1.

Conjectures from Colin Barker, Nov 12 2018: (Start)

G.f.: x*(172 + 2861*x + 4335*x^2 - 2703*x^3 - 2357*x^4 + 227*x^5 + 65*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:
..1....1....0....2....2....1....0....1....1....1....1....1....0....0....1....0
..4....1....0....2....1....4....2....2....2....2....0....2....2....1....3....4
..2....0....2....0....1....0....2....1....1....3....2....2....4....2....1....4
..3....1....4....4....3....4....2....2....0....3....4....2....2....2....2....4
..2....1....3....3....2....2....4....2....1....3....3....0....0....2....1....4
..0....2....2....0....2....2....3....3....4....4....2....4....4....3....1....4
..2....2....2....2....4....2....1....4....1....1....2....2....2....2....1....2
..4....0....1....2....0....4....1....0....3....0....1....2....2....4....1....4
..0....1....1....1....0....0....2....2....0....3....1....3....3....1....0....4

Crossrefs

Row 4 of A250336.

Sequence in context: A214115 A250968 A264213 * A035828 A259017 A097845

Adjacent sequences: A250337 A250338 A250339 * A250341 A250342 A250343

Keyword

nonn

Author

R. H. Hardin, Nov 19 2014

Status

approved