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Number of length-n 0..4 arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.
1

%I #4 Feb 04 2016 22:01:29

%S 5,25,121,581,2776,13204,62535,294967,1385969,6488635,30273074,

%T 140779986,652648100,3016745162,13905372533,63924885355,293126854872,

%U 1340883359460,6119617278729,27867658231717,126637380509476,574312506857594

%N Number of length-n 0..4 arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

%C Column 4 of A268457.

%H R. H. Hardin, <a href="/A268453/b268453.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 39*a(n-1) -693*a(n-2) +7441*a(n-3) -54053*a(n-4) +282341*a(n-5) -1103223*a(n-6) +3324255*a(n-7) -7938129*a(n-8) +15426103*a(n-9) -25019179*a(n-10) +34622055*a(n-11) -41606078*a(n-12) +43991906*a(n-13) -41304450*a(n-14) +34649044*a(n-15) -26064185*a(n-16) +17607461*a(n-17) -10675286*a(n-18) +5792770*a(n-19) -2798790*a(n-20) +1194342*a(n-21) -444872*a(n-22) +142204*a(n-23) -38049*a(n-24) +8201*a(n-25) -1336*a(n-26) +146*a(n-27) -8*a(n-28)

%e Some solutions for n=7

%e ..4....4....4....0....2....2....1....0....1....3....3....2....2....4....1....2

%e ..0....0....0....3....3....0....4....4....1....3....1....1....4....3....0....1

%e ..1....3....1....2....3....0....4....1....4....1....2....0....4....3....0....1

%e ..4....0....1....2....3....0....2....2....4....4....2....4....2....3....0....3

%e ..2....1....1....2....4....4....1....2....0....2....4....3....4....3....2....1

%e ..2....3....2....1....4....4....4....2....0....1....2....2....0....0....2....3

%e ..2....2....4....2....0....1....3....0....0....0....4....3....0....4....0....0

%Y Cf. A268457.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 04 2016