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A251423 Number of length n+2 0..3 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

%I A251423 #6 Jul 23 2025 13:19:46
%S A251423 16,116,380,1888,7458,31980,127566,520568,2080650,8370976,33475854,
%T A251423 134136344,536498498,2147099168,8588150878,34357874584,137430314336,
%U A251423 549746688148,2198981195384,8796047678504,35184165954884,140737260054372
%N A251423 Number of length n+2 0..3 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
%C A251423 Column 3 of A251428
%H A251423 R. H. Hardin, <a href="/A251423/b251423.txt">Table of n, a(n) for n = 1..109</a>
%F A251423 Empirical: a(n) = 11*a(n-1) -40*a(n-2) +28*a(n-3) +156*a(n-4) -332*a(n-5) +89*a(n-6) -263*a(n-7) +2117*a(n-8) -2247*a(n-9) -4433*a(n-10) +9779*a(n-11) -1921*a(n-12) +1315*a(n-13) -27632*a(n-14) +27440*a(n-15) +35510*a(n-16) -66532*a(n-17) +23084*a(n-18) -38208*a(n-19) +116256*a(n-20) -72640*a(n-21) -64384*a(n-22) +115840*a(n-23) -109312*a(n-24) +125184*a(n-25) -120064*a(n-26) +72704*a(n-27) -25600*a(n-28) +4096*a(n-29)
%e A251423 Some solutions for n=7
%e A251423 ..2....0....2....2....2....1....0....3....1....1....2....1....0....0....1....0
%e A251423 ..2....3....3....0....3....2....2....1....0....1....2....1....0....0....0....0
%e A251423 ..2....0....3....2....1....0....2....1....1....3....3....3....0....1....2....0
%e A251423 ..1....3....3....3....1....1....0....3....1....0....2....0....1....3....2....1
%e A251423 ..0....2....2....3....0....2....3....2....1....2....3....3....3....2....1....3
%e A251423 ..2....2....3....0....2....0....0....2....3....1....1....0....1....1....1....3
%e A251423 ..1....2....2....1....1....1....2....2....0....0....0....3....2....1....1....2
%e A251423 ..0....2....2....2....0....0....2....1....2....3....3....0....2....0....1....2
%e A251423 ..1....2....3....0....3....1....3....0....1....2....3....2....1....2....1....2
%K A251423 nonn
%O A251423 1,1
%A A251423 _R. H. Hardin_, Dec 02 2014