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A241613 Number of length n+2 0..7 arrays with no consecutive three elements summing to more than 7.

%I A241613 #9 Jun 09 2025 00:40:14
%S A241613 120,540,2430,10242,44274,193194,835812,3617703,15692003,68014233,
%T A241613 294705961,1277336862,5536267273,23993714457,103989408537,
%U A241613 450697682809,1953337206374,8465825120096,36691243404754,159021259038334
%N A241613 Number of length n+2 0..7 arrays with no consecutive three elements summing to more than 7.
%H A241613 R. H. Hardin, <a href="/A241613/b241613.txt">Table of n, a(n) for n = 1..210</a>
%F A241613 Empirical: a(n) = 3*a(n-1) +2*a(n-2) +25*a(n-3) -23*a(n-4) -32*a(n-5) -160*a(n-6) +84*a(n-7) +98*a(n-8) +497*a(n-9) -235*a(n-10) -176*a(n-11) -895*a(n-12) +423*a(n-13) +219*a(n-14) +1112*a(n-15) -491*a(n-16) -173*a(n-17) -971*a(n-18) +376*a(n-19) +116*a(n-20) +624*a(n-21) -213*a(n-22) -61*a(n-23) -305*a(n-24) +82*a(n-25) +23*a(n-26) +107*a(n-27) -27*a(n-28) -5*a(n-29) -32*a(n-30) +5*a(n-31) +a(n-32) +5*a(n-33) -a(n-34) -a(n-36).
%e A241613 Some solutions for n=5:
%e A241613 ..0....0....0....3....3....0....0....2....1....0....3....1....5....1....2....3
%e A241613 ..5....2....4....0....0....0....1....0....2....6....1....0....0....0....1....0
%e A241613 ..0....1....1....0....3....3....3....0....3....1....3....2....2....3....1....0
%e A241613 ..0....1....0....1....2....4....2....0....1....0....0....3....2....4....3....1
%e A241613 ..0....3....5....2....0....0....2....3....2....1....0....2....2....0....2....3
%e A241613 ..2....0....0....0....3....0....1....2....2....4....1....0....1....2....1....0
%e A241613 ..5....1....1....4....4....4....0....1....1....1....2....2....1....1....3....3
%Y A241613 Column 7 of A241619.
%K A241613 nonn
%O A241613 1,1
%A A241613 _R. H. Hardin_, Apr 26 2014