A250387 T(n,k)=Number of length n+3 0..k arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms.

6, 42, 6, 156, 78, 6, 420, 432, 146, 6, 930, 1560, 1208, 274, 6, 1806, 4350, 5848, 3384, 514, 6, 3192, 10206, 20518, 21950, 9480, 966, 6, 5256, 21168, 58114, 96866, 82398, 26578, 1816, 6, 8190, 40032, 141344, 331128, 457366, 309452, 74528, 3414, 6, 12210

Offset

1,1

Comments

Table starts

.6....42.....156......420........930........1806........3192.........5256

.6....78.....432.....1560.......4350.......10206.......21168........40032

.6...146....1208.....5848......20518.......58114......141344.......306816

.6...274....3384....21950......96866......331128......944272......2352468

.6...514....9480....82398.....457366.....1886948.....6308960.....18038628

.6...966...26578...309452....2160160....10755158....42158796....138336744

.6..1816...74528..1162292...10203222....61304844...281731072...1060924200

.6..3414..208998..4365720...48194820...349446100..1882722300...8136444312

.6..6418..586102.16398414..227649458..1991900312.12581692558..62400176438

.6.12066.1643650.61595866.1075313612.11354195442.84080003928.478561255176

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical for column k, apparently recurrence of order 7*k-4:

k=1: a(n) = a(n-1)

k=2: a(n) = a(n-1) +2*a(n-2) -a(n-3) +3*a(n-4) -a(n-5) -7*a(n-6) +a(n-7) +a(n-10)

k=3: [order 17]

k=4: [order 24]

k=5: [order 31]

k=6: [order 38]

k=7: [order 45]

Empirical for row n, apparently polynomial of degree n+3:

n=1: a(n) = n^4 + 2*n^3 + 2*n^2 + n

n=2: a(n) = n^5 + (3/2)*n^4 + 2*n^3 + (3/2)*n^2

n=3: a(n) = n^6 + (16/15)*n^5 + (13/6)*n^4 + (5/3)*n^3 - (1/6)*n^2 + (4/15)*n

n=4: [polynomial of degree 7]

n=5: [polynomial of degree 8]

n=6: [polynomial of degree 9]

n=7: [polynomial of degree 10]

Example

Some solutions for n=4 k=4
..3....4....1....4....0....4....2....1....1....1....0....0....1....3....4....0
..2....2....2....2....1....0....3....2....4....3....1....0....1....0....0....3
..3....3....0....4....2....2....4....3....3....2....3....3....0....3....4....0
..1....1....0....2....3....1....0....0....2....4....2....2....0....0....0....2
..3....0....4....3....4....4....4....1....4....1....3....1....1....4....2....1
..0....4....4....2....4....0....1....0....4....4....0....3....2....0....3....4
..4....2....2....3....2....3....0....2....3....0....0....4....2....1....0....1

Crossrefs

Row 1 is A082986

Sequence in context: A181041 A109856 A249135 * A306429 A117693 A153243

Adjacent sequences: A250384 A250385 A250386 * A250388 A250389 A250390

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 20 2014

Status

approved