cp's OEIS Frontend

A221576 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by something other than 1.

%I A221576 #8 Aug 08 2018 18:37:20
%S A221576 10,141,1210,5913,20944,59705,145800,317233,631328,1170369,2047960,
%T A221576 3416105,5473008,8471593,12728744,18635265,26666560,37394033,51497208,
%U A221576 69776569,93167120,122752665,159780808,205678673,262069344,330789025
%N A221576 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by something other than 1.
%C A221576 Row 6 of A221573.
%H A221576 R. H. Hardin, <a href="/A221576/b221576.txt">Table of n, a(n) for n = 1..210</a>
%F A221576 Empirical: a(n) = 1*n^6 + 2*n^5 - 5*n^4 + 24*n^3 - 41*n^2 + 50*n - 31 for n>3.
%F A221576 Conjectures from _Colin Barker_, Aug 08 2018: (Start)
%F A221576 G.f.: x*(10 + 71*x + 433*x^2 + 54*x^3 + 378*x^4 - 355*x^5 + 193*x^6 - 80*x^7 + 18*x^8 - 2*x^9) / (1 - x)^7.
%F A221576 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 A221576 (End)
%e A221576 Some solutions for n=6:
%e A221576 ..6....3....0....1....4....6....5....2....1....6....0....4....6....3....5....3
%e A221576 ..1....0....6....3....4....4....1....4....3....3....0....1....6....0....1....5
%e A221576 ..1....1....1....3....2....1....3....6....2....6....1....4....6....6....3....0
%e A221576 ..4....4....2....6....4....4....0....3....2....1....4....2....3....4....3....6
%e A221576 ..3....6....6....2....0....0....2....3....0....0....0....6....6....4....3....2
%e A221576 ..0....4....6....2....2....3....6....0....5....3....6....0....6....2....5....6
%Y A221576 Cf. A221573.
%K A221576 nonn
%O A221576 1,1
%A A221576 _R. H. Hardin_, Jan 20 2013