A254698 T(n,k)=Number of length n+4 0..k arrays with every five consecutive terms having the maximum of some two terms equal to the minimum of the remaining three terms

22, 133, 34, 464, 267, 54, 1205, 1116, 552, 86, 2606, 3341, 2764, 1140, 136, 4977, 8142, 9507, 6808, 2310, 212, 8688, 17255, 25962, 26759, 16276, 4542, 334, 14169, 33048, 60634, 81390, 72271, 37204, 9106, 532, 21910, 58617, 126456, 208114, 242076

Offset

1,1

Comments

Table starts

...22...133.....464.....1205.....2606......4977......8688......14169......21910

...34...267....1116.....3341.....8142.....17255.....33048......58617......97882

...54...552....2764.....9507....25962.....60634....126456.....242037.....433054

...86..1140....6808....26759....81390....208114....469376.....962541....1831798

..136..2310...16276....72271...242076....670372...1618264....3520845....7060672

..212..4542...37204...183491...665256...1961608...4985336...11325573...23567212

..334..9106...87892...489135..1954106...6255136..17080712...41376909...91273510

..532.18498..211672..1335839..5903724..20574928..60483408..156403629..365868388

..852.37742..512684..3667545.17914000..67894218.214599288..591634473.1465804300

.1367.77010.1241154.10039379.54038937.222047516.752272724.2204108901.5765156683

Links

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

Formula

Empirical for column k:

k=1: [linear recurrence of order 15]

k=2: [order 49]

k=3: [order 83]

Empirical for row n:

n=1: a(n) = (5/2)*n^4 + (20/3)*n^3 + (15/2)*n^2 + (13/3)*n + 1

n=2: a(n) = (4/5)*n^5 + (19/3)*n^4 + (34/3)*n^3 + (29/3)*n^2 + (73/15)*n + 1

n=3: [polynomial of degree 6]

n=4: [polynomial of degree 7]

n=5: [polynomial of degree 7]

n=6: [polynomial of degree 7]

n=7: [polynomial of degree 8]

Example

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

Crossrefs

Sequence in context: A233060 A299520 A003778 * A041936 A254699 A183909

Adjacent sequences: A254695 A254696 A254697 * A254699 A254700 A254701

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 05 2015

Status

approved