cp's OEIS Frontend

A221516 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more, starting with 0.

%I A221516 #7 Aug 06 2018 05:35:41
%S A221516 0,3,30,130,381,884,1765,3174,5285,8296,12429,17930,25069,34140,45461,
%T A221516 59374,76245,96464,120445,148626,181469,219460,263109,312950,369541,
%U A221516 433464,505325,585754,675405,774956,885109,1006590,1140149,1286560
%N A221516 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more, starting with 0.
%C A221516 Row 5 of A221515.
%H A221516 R. H. Hardin, <a href="/A221516/b221516.txt">Table of n, a(n) for n = 1..210</a>
%F A221516 Empirical: a(n) = 1*n^4 - 1*n^3 - 10*n^2 + 33*n - 34 for n>3.
%F A221516 Conjectures from _Colin Barker_, Aug 06 2018: (Start)
%F A221516 G.f.: x^2*(3 + 15*x + 10*x^2 + x^3 - 6*x^4 + 2*x^5 - x^6) / (1 - x)^5.
%F A221516 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>8.
%F A221516 (End)
%e A221516 Some solutions for n=6:
%e A221516 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221516 ..3....6....3....6....4....2....3....2....5....4....4....6....2....6....6....2
%e A221516 ..5....2....4....2....6....3....3....0....6....1....0....0....0....4....5....3
%e A221516 ..4....4....6....6....5....5....0....6....0....0....5....4....4....2....1....6
%e A221516 ..6....6....4....4....0....3....4....1....2....5....0....2....0....4....4....0
%Y A221516 Cf. A221515.
%K A221516 nonn
%O A221516 1,2
%A A221516 _R. H. Hardin_, Jan 18 2013