cp's OEIS Frontend

A221577 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by something other than 1.

%I A221577 #7 Aug 08 2018 15:10:29
%S A221577 16,345,4240,26911,117104,395641,1116400,2754635,6127696,12553189,
%T A221577 24049616,43584535,75375280,125247281,201055024,313170691,475045520,
%U A221577 703848925,1021190416,1453929359,2035077616,2804800105,3811518320
%N A221577 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by something other than 1.
%C A221577 Row 7 of A221573.
%H A221577 R. H. Hardin, <a href="/A221577/b221577.txt">Table of n, a(n) for n = 1..210</a>
%F A221577 Empirical: a(n) = 1*n^7 + 3*n^6 - 7*n^5 + 29*n^4 - 41*n^3 + 45*n^2 - 33*n + 19 for n>2.
%F A221577 Conjectures from _Colin Barker_, Aug 08 2018: (Start)
%F A221577 G.f.: x*(16 + 217*x + 1928*x^2 + 1755*x^3 + 2336*x^4 - 1869*x^5 + 1096*x^6 - 579*x^7 + 160*x^8 - 20*x^9) / (1 - x)^8.
%F A221577 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 A221577 (End)
%e A221577 Some solutions for n=6:
%e A221577 ..0....4....3....0....4....4....4....3....0....0....3....4....0....0....0....4
%e A221577 ..2....0....3....3....0....4....0....0....3....6....0....0....6....0....5....0
%e A221577 ..2....1....5....4....6....0....5....2....1....2....1....5....2....3....0....0
%e A221577 ..3....6....2....6....4....2....3....0....0....5....4....2....4....5....4....0
%e A221577 ..0....1....5....0....4....4....2....4....0....6....4....4....1....1....4....0
%e A221577 ..2....3....5....2....6....1....4....2....3....6....3....2....4....1....4....4
%e A221577 ..4....1....5....5....6....6....2....2....6....6....1....4....4....5....0....2
%Y A221577 Cf. A221573.
%K A221577 nonn
%O A221577 1,1
%A A221577 _R. H. Hardin_, Jan 20 2013