cp's OEIS Frontend

A221466 Number of 0..n arrays of length 7 with each element unequal to at least one neighbor, starting with 0.

%I A221466 #8 Aug 05 2018 15:06:02
%S A221466 8,240,1944,8960,30000,81648,192080,405504,787320,1430000,2459688,
%T A221466 4043520,6397664,9796080,14580000,21168128,30067560,41885424,57341240,
%U A221466 77280000,102685968,134697200,174620784,223948800,284375000,357812208
%N A221466 Number of 0..n arrays of length 7 with each element unequal to at least one neighbor, starting with 0.
%C A221466 Row 7 of A221463.
%H A221466 R. H. Hardin, <a href="/A221466/b221466.txt">Table of n, a(n) for n = 1..135</a>
%F A221466 Empirical: a(n) = 1*n^6 + 4*n^5 + 3*n^4.
%F A221466 Conjectures from _Colin Barker_, Aug 05 2018: (Start)
%F A221466 G.f.: 8*x*(1 + 23*x + 54*x^2 + 14*x^3 - 2*x^4) / (1 - x)^7.
%F A221466 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>7.
%F A221466 (End)
%e A221466 Some solutions for n=6:
%e A221466 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221466 ..6....4....5....2....5....2....4....4....4....4....1....3....4....6....2....3
%e A221466 ..6....4....0....2....4....0....4....3....3....4....2....4....5....4....1....2
%e A221466 ..0....5....6....4....0....4....2....6....3....5....2....6....2....6....6....1
%e A221466 ..0....3....1....2....1....4....0....4....6....2....0....1....3....5....4....1
%e A221466 ..6....6....1....3....0....3....2....4....6....0....2....0....6....4....4....0
%e A221466 ..2....2....6....0....6....1....1....3....3....3....5....3....5....6....5....4
%Y A221466 Cf. A221463.
%K A221466 nonn
%O A221466 1,1
%A A221466 _R. H. Hardin_, Jan 17 2013