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%I #6 Sep 23 2014 16:41:24
%S 168,456,1248,3424,9392,25822,71060,195536,537880,1480026,4073228,
%T 11209522,30845400,84880220,233584180,642804172,1768901108,4867756146,
%U 13395492168,36862857286,101441854028,279154735896,768198993968
%N Number of length n+3 0..3 arrays with no disjoint pairs in any consecutive four terms having the same sum
%C Column 3 of A247726
%H R. H. Hardin, <a href="/A247721/b247721.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) -3*a(n-2) +8*a(n-3) +16*a(n-4) -8*a(n-5) +46*a(n-6) -48*a(n-7) -25*a(n-8) -38*a(n-10) +62*a(n-11) -58*a(n-12) +72*a(n-13) -354*a(n-14) +246*a(n-15) -26*a(n-16) +162*a(n-17) -183*a(n-18) -112*a(n-19) -34*a(n-20) +112*a(n-21) +320*a(n-22) -166*a(n-23) -80*a(n-24) -90*a(n-25) -12*a(n-26) +72*a(n-27).
%F Empirical g.f.: -2*x*(84 +60*x +420*x^2 +687*x^5 -784*x^12 +7433*x^21 -1924*x^6 -983*x^7+2304*x^26 -394*x^8 +564*x^25 +6460*x^20 -6844*x^22 -2604*x^24 -911*x^9 -3644*x^23 -24*x^15+1603*x^19 -2826*x^18 -2238*x^11 -6952*x^17 -24*x^4 +1024*x^10 -8176*x^13 +7852*x^14 +476*x^3 +2294*x^16) / ( -1 +2*x -3*x^2 -8*x^5 -58*x^12 +112*x^21 +46*x^6 -48*x^7 -12*x^26 -25*x^8 -90*x^25 -34*x^20 +320*x^22 -80*x^24 -166*x^23 +246*x^15 -112*x^19 -183*x^18 +62*x^11 +162*x^17 +16*x^4 -38*x^10 +72*x^27 +72*x^13 -354*x^14 +8*x^3 -26*x^16 ). - _R. J. Mathar_, Sep 23 2014
%e Some solutions for n=6
%e ..0....0....3....3....1....2....1....0....2....1....1....2....2....1....3....3
%e ..1....0....2....3....2....3....3....2....1....1....1....2....3....3....3....0
%e ..0....2....0....0....0....1....1....0....3....3....0....3....3....1....1....2
%e ..3....3....3....2....2....1....2....0....3....2....3....0....1....0....0....0
%e ..3....0....2....2....3....1....3....0....0....3....3....2....3....1....0....0
%e ..3....2....3....3....0....0....1....1....3....1....3....2....0....3....2....0
%e ..0....0....0....0....3....1....3....2....3....3....1....1....1....0....0....2
%e ..3....0....3....0....1....3....0....2....2....0....3....0....0....0....0....1
%e ..3....1....3....2....0....1....3....0....1....1....3....0....2....0....0....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 23 2014
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