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A241612 Number of length n+2 0..6 arrays with no consecutive three elements summing to more than 6.

%I A241612 #6 Jun 02 2025 10:10:28
%S A241612 84,336,1344,5040,19374,75180,289248,1113348,4294574,16553380,
%T A241612 63784786,245853464,947613919,3652200016,14076313291,54253546534,
%U A241612 209104275023,805930938847,3106231773354,11972077046301,46142909963825
%N A241612 Number of length n+2 0..6 arrays with no consecutive three elements summing to more than 6.
%C A241612 Column 6 of A241619
%H A241612 R. H. Hardin, <a href="/A241612/b241612.txt">Table of n, a(n) for n = 1..210</a>
%F A241612 Empirical: a(n) = 3*a(n-1) +a(n-2) +16*a(n-3) -20*a(n-4) -18*a(n-5) -65*a(n-6) +65*a(n-7) +41*a(n-8) +132*a(n-9) -130*a(n-10) -49*a(n-11) -144*a(n-12) +153*a(n-13) +31*a(n-14) +113*a(n-15) -115*a(n-16) -11*a(n-17) -60*a(n-18) +55*a(n-19) +4*a(n-20) +23*a(n-21) -21*a(n-22) -a(n-23) -5*a(n-24) +4*a(n-25) +a(n-27) -a(n-28)
%e A241612 Some solutions for n=5
%e A241612 ..0....3....0....3....4....1....2....3....4....1....3....4....2....4....0....2
%e A241612 ..0....2....1....0....1....1....0....0....0....5....2....1....0....0....0....3
%e A241612 ..1....1....3....0....1....4....1....1....2....0....1....0....2....1....3....0
%e A241612 ..3....0....1....3....3....0....1....1....0....1....1....2....3....3....0....3
%e A241612 ..0....1....0....0....0....0....0....3....0....1....2....0....1....1....2....2
%e A241612 ..3....1....2....0....2....1....4....0....0....0....0....0....1....1....4....1
%e A241612 ..2....2....4....0....4....3....0....0....3....4....0....1....1....3....0....3
%K A241612 nonn
%O A241612 1,1
%A A241612 _R. H. Hardin_, Apr 26 2014