A221541 - OEIS

%I #8 Oct 18 2017 18:23:32

%S 0,7,44,350,2658,20386,156098,1195561,9156379,70126074,537074685,

%T 4113296146,31502516844,241268447450,1847803587081,14151780448318,

%U 108384295414048,830083220654363,6357361558503534,48689149448999134

%N Number of 0..7 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

%C Column 7 of A221542.

%H R. H. Hardin, <a href="/A221541/b221541.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) +4*a(n-2) +5*a(n-3) +20*a(n-4) +20*a(n-5) +23*a(n-6) -6*a(n-7) +3*a(n-8).

%F Empirical g.f.: x^2*(7 - 5*x + 14*x^2 - 3*x^3 + 20*x^4 - 6*x^5) / (1 - 7*x - 4*x^2 - 5*x^3 - 20*x^4 - 20*x^5 - 23*x^6 + 6*x^7 - 3*x^8). - _Colin Barker_, Oct 18 2017

%e Some solutions for n=6

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..4....7....6....3....0....4....3....2....0....0....0....2....4....2....3....4

%e ..2....5....3....2....6....1....4....7....3....4....6....6....0....5....2....1

%e ..4....6....6....4....6....4....1....0....6....4....5....6....2....0....0....7

%e ..4....2....7....1....7....3....7....2....3....0....5....6....2....6....4....4

%e ..6....7....5....7....4....6....4....6....0....3....5....1....7....2....0....1

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2013