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A249705 Number of length n+3 0..6 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

%I A249705 #6 Jul 23 2025 12:06:18
%S A249705 595,1729,4893,12789,29673,75495,200489,528755,1341901,3434085,
%T A249705 8949133,23454657,60890031,157756415,410782645,1074162701,2805580083,
%U A249705 7318553467,19112582503,50014143783,130956449801,342843638551,897866650281
%N A249705 Number of length n+3 0..6 arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.
%C A249705 Column 6 of A249707
%H A249705 R. H. Hardin, <a href="/A249705/b249705.txt">Table of n, a(n) for n = 1..210</a>
%F A249705 Empirical: a(n) = 4*a(n-1) -3*a(n-2) -5*a(n-3) +77*a(n-4) -188*a(n-5) -44*a(n-6) +328*a(n-7) -2041*a(n-8) +2681*a(n-9) +4824*a(n-10) -4044*a(n-11) +25336*a(n-12) -7463*a(n-13) -80625*a(n-14) -21968*a(n-15) -198280*a(n-16) -135500*a(n-17) +551797*a(n-18) +646315*a(n-19) +1307173*a(n-20) +1558772*a(n-21) -1777441*a(n-22) -4439396*a(n-23) -6651096*a(n-24) -8197360*a(n-25) +1807976*a(n-26) +15419208*a(n-27) +21844724*a(n-28) +23090640*a(n-29) +3731760*a(n-30) -28712880*a(n-31) -41155200*a(n-32) -32803200*a(n-33) -6163200*a(n-34) +27648000*a(n-35) +31104000*a(n-36) +10368000*a(n-37)
%e A249705 Some solutions for n=6
%e A249705 ..2....3....4....6....4....1....3....5....3....2....2....6....1....0....0....2
%e A249705 ..5....2....3....1....4....4....4....1....4....3....3....0....3....5....5....1
%e A249705 ..5....3....6....1....3....4....2....0....6....4....2....4....5....5....5....6
%e A249705 ..5....3....4....1....5....5....3....1....4....3....1....4....3....5....6....2
%e A249705 ..1....6....4....0....4....3....3....1....4....3....2....4....3....5....5....2
%e A249705 ..5....3....4....6....4....4....3....1....2....3....2....4....3....5....5....2
%e A249705 ..5....3....1....1....2....4....6....4....4....3....6....1....3....1....5....2
%e A249705 ..5....0....6....1....5....6....3....1....4....0....2....4....3....5....5....3
%e A249705 ..3....3....4....0....4....3....2....1....6....5....1....5....3....5....3....0
%K A249705 nonn
%O A249705 1,1
%A A249705 _R. H. Hardin_, Nov 04 2014