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%I #4 Feb 05 2015 21:06:00
%S 22,133,34,464,267,54,1205,1116,552,86,2606,3341,2764,1140,136,4977,
%T 8142,9507,6808,2310,212,8688,17255,25962,26759,16276,4542,334,14169,
%U 33048,60634,81390,72271,37204,9106,532,21910,58617,126456,208114,242076
%N 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
%C Table starts
%C ...22...133.....464.....1205.....2606......4977......8688......14169......21910
%C ...34...267....1116.....3341.....8142.....17255.....33048......58617......97882
%C ...54...552....2764.....9507....25962.....60634....126456.....242037.....433054
%C ...86..1140....6808....26759....81390....208114....469376.....962541....1831798
%C ..136..2310...16276....72271...242076....670372...1618264....3520845....7060672
%C ..212..4542...37204...183491...665256...1961608...4985336...11325573...23567212
%C ..334..9106...87892...489135..1954106...6255136..17080712...41376909...91273510
%C ..532.18498..211672..1335839..5903724..20574928..60483408..156403629..365868388
%C ..852.37742..512684..3667545.17914000..67894218.214599288..591634473.1465804300
%C .1367.77010.1241154.10039379.54038937.222047516.752272724.2204108901.5765156683
%H R. H. Hardin, <a href="/A254698/b254698.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 15]
%F k=2: [order 49]
%F k=3: [order 83]
%F Empirical for row n:
%F n=1: a(n) = (5/2)*n^4 + (20/3)*n^3 + (15/2)*n^2 + (13/3)*n + 1
%F n=2: a(n) = (4/5)*n^5 + (19/3)*n^4 + (34/3)*n^3 + (29/3)*n^2 + (73/15)*n + 1
%F n=3: [polynomial of degree 6]
%F n=4: [polynomial of degree 7]
%F n=5: [polynomial of degree 7]
%F n=6: [polynomial of degree 7]
%F n=7: [polynomial of degree 8]
%e Some solutions for n=4 k=4
%e ..1....2....3....2....0....3....4....0....3....4....4....1....3....4....4....2
%e ..0....0....0....2....4....0....2....4....1....0....3....4....3....1....1....3
%e ..4....2....2....3....0....4....3....1....1....4....3....0....0....0....3....4
%e ..1....2....2....2....3....2....4....1....3....2....3....1....2....0....3....3
%e ..3....3....2....4....0....2....3....1....1....2....1....1....2....0....3....3
%e ..1....3....4....2....0....4....3....2....1....3....3....3....4....1....3....3
%e ..1....2....0....2....0....2....3....1....0....1....3....1....2....2....3....3
%e ..2....2....4....0....1....4....2....4....2....3....3....0....2....0....3....0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 05 2015