cp's OEIS Frontend

A221527 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 2 or more.

%I A221527 #8 Aug 06 2018 08:22:06
%S A221527 0,16,768,8544,50400,205080,654864,1763328,4184064,9005400,17936160,
%T A221527 33537504,59505888,101012184,165102000,261162240,401458944,601751448,
%U A221527 881987904,1267087200,1787812320,2481740184,3394333008,4580116224
%N A221527 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 2 or more.
%C A221527 Row 7 of A221524.
%H A221527 R. H. Hardin, <a href="/A221527/b221527.txt">Table of n, a(n) for n = 1..210</a>
%F A221527 Empirical: a(n) = 1*n^7 + 1*n^6 - 29*n^5 + 109*n^4 - 204*n^3 + 202*n^2 - 80*n for n>2.
%F A221527 Conjectures from _Colin Barker_, Aug 06 2018: (Start)
%F A221527 G.f.: 8*x^2*(2 + 80*x + 356*x^2 + 332*x^3 - 97*x^4 - 22*x^5 - 28*x^6 + 8*x^7 - x^8) / (1 - x)^8.
%F A221527 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>10.
%F A221527 (End)
%e A221527 Some solutions for n=6:
%e A221527 ..4....3....4....4....0....0....3....3....3....1....4....3....3....3....4....0
%e A221527 ..1....5....1....6....4....5....1....0....1....3....2....6....0....0....0....6
%e A221527 ..1....1....6....1....5....1....6....3....0....3....1....4....6....5....0....4
%e A221527 ..3....5....3....0....0....6....5....0....6....5....4....2....0....3....2....6
%e A221527 ..6....2....2....5....5....0....1....2....3....0....0....1....2....5....6....3
%e A221527 ..0....0....4....2....3....6....5....3....1....4....0....6....2....0....1....2
%e A221527 ..4....5....6....5....0....2....3....1....4....1....6....2....5....5....3....4
%Y A221527 Cf. A221524.
%K A221527 nonn
%O A221527 1,2
%A A221527 _R. H. Hardin_, Jan 19 2013