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%I #6 Apr 21 2024 22:37:30
%S 343,1799,9156,46914,217856,974944,4350588,18667931,77880418,
%T 322089271,1307443907,5208681584,20546907053,80150786624,308819454899,
%U 1179461682136,4468650085856,16786704855127,62609587475559
%N Number of length n+2 0..6 arrays with the medians of every three consecutive terms nondecreasing.
%C Column 6 of A250140.
%H R. H. Hardin, <a href="/A250138/b250138.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) -21*a(n-2) +147*a(n-3) -672*a(n-4) +1526*a(n-5) -7399*a(n-6) +25649*a(n-7) -42973*a(n-8) +192307*a(n-9) -514173*a(n-10) +575399*a(n-11) -3074566*a(n-12) +5772926*a(n-13) -3135200*a(n-14) +33671364*a(n-15) -31736296*a(n-16) -6174074*a(n-17) -268252277*a(n-18) -22436585*a(n-19) +124952727*a(n-20) +1541722905*a(n-21) +1602276594*a(n-22) +140604582*a(n-23) -5840564831*a(n-24) -11203950193*a(n-25) -7301869176*a(n-26) +11531631728*a(n-27) +38571124984*a(n-28) +41463778840*a(n-29) +1826080960*a(n-30) -68505468224*a(n-31) -106915234608*a(n-32) -60747512976*a(n-33) +46128994560*a(n-34) +130831309440*a(n-35) +115397395200*a(n-36) +23935046400*a(n-37) -56194560000*a(n-38) -71456256000*a(n-39) -37324800000*a(n-40) -7464960000*a(n-41).
%e Some solutions for n=4
%e ..5....2....1....6....2....5....2....4....4....6....2....3....3....0....0....6
%e ..0....1....1....4....5....0....0....0....2....2....0....1....1....6....1....5
%e ..0....0....6....2....4....3....3....2....2....0....6....4....6....2....6....5
%e ..1....4....1....5....4....5....5....2....5....6....5....4....3....2....1....6
%e ..4....6....4....4....2....6....2....2....5....4....3....4....4....4....3....5
%e ..0....5....5....5....4....5....5....3....5....4....5....1....4....2....6....5
%Y Cf. A250140.
%K nonn,changed
%O 1,1
%A _R. H. Hardin_, Nov 13 2014
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