|
%I #8 Aug 06 2018 07:25:21
%S 0,8,248,2088,9940,33860,92934,219352,463208,898020,1626970,2789864,
%T 4570812,7206628,10995950,16309080,23598544,33410372,46396098,
%U 63325480,85099940,112766724,147533782,190785368,244098360,309259300,388282154
%N Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 2 or more, starting with 0.
%C Row 7 of A221515.
%H R. H. Hardin, <a href="/A221518/b221518.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 1*n^6 + 1*n^5 - 29*n^4 + 104*n^3 - 173*n^2 + 136*n - 40 for n>3.
%F Conjectures from _Colin Barker_, Aug 06 2018: (Start)
%F G.f.: 2*x^2*(4 + 96*x + 260*x^2 + 126*x^3 - 136*x^4 + 43*x^5 - 49*x^6 + 19*x^7 - 3*x^8) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.
%F (End)
%e Some solutions for n=6:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..6....5....3....5....5....4....3....5....6....6....3....6....6....6....3....5
%e ..0....1....0....1....0....6....5....5....2....5....6....1....2....0....0....6
%e ..5....1....2....4....2....6....2....1....4....2....6....0....1....2....5....0
%e ..2....5....4....0....4....0....6....5....2....6....0....6....5....5....1....0
%e ..6....6....5....2....5....0....2....2....4....3....3....5....5....0....6....4
%e ..0....4....2....6....0....2....4....0....1....5....1....3....2....5....3....6
%Y Cf. A221515.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 18 2013
| 