|
%I #8 Oct 30 2018 20:20:04
%S 41,556,4175,21631,86828,289248,835812,2159025,5093737,11151140,
%T 22925695,44678543,83149600,148659968,256576512,429221457,698321649,
%U 1108104700,1719162599,2613217519,3898939484,5718981280,8258412500,11754751905
%N Number of length 7+2 0..n arrays with no consecutive three elements summing to more than n.
%H R. H. Hardin, <a href="/A241622/b241622.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (131/60480)*n^9 + (131/3360)*n^8 + (3137/10080)*n^7 + (347/240)*n^6 + (12407/2880)*n^5 + (4097/480)*n^4 + (169957/15120)*n^3 + (7963/840)*n^2 + (487/105)*n + 1.
%F Conjectures from _Colin Barker_, Oct 30 2018: (Start)
%F G.f.: x*(41 + 146*x + 460*x^2 - 19*x^3 + 283*x^4 - 209*x^5 + 120*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.
%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
%F (End)
%e Some solutions for n=5:
%e ..3....2....1....1....2....0....2....2....1....4....3....0....0....3....1....2
%e ..0....1....1....1....0....2....0....1....2....1....0....2....5....0....2....2
%e ..0....1....2....2....0....2....1....1....1....0....1....0....0....0....0....1
%e ..0....0....2....1....0....1....2....1....0....1....1....1....0....1....2....2
%e ..2....4....0....2....3....1....2....1....3....0....0....0....1....0....0....1
%e ..1....0....0....0....1....3....0....0....1....2....1....1....0....1....2....2
%e ..2....0....2....0....1....0....0....3....0....0....3....1....1....0....0....1
%e ..0....0....2....1....3....2....0....0....3....0....0....0....4....2....3....0
%e ..3....2....1....1....0....3....4....2....2....3....1....3....0....3....2....4
%Y Row 7 of A241619.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 26 2014
| 