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A212841 Number of 0..n arrays of length 8 with 0 never adjacent to n.

%I A212841 #10 Jul 21 2018 10:07:36
%S A212841 2,1393,28642,231521,1168786,4414417,13667858,36590017,87627106,
%T A212841 192124721,392074882,753879073,1378550642,2414820241,4075648306,
%U A212841 6658688897,10571289538,16360652017,24749819426,36680195041,53361338962
%N A212841 Number of 0..n arrays of length 8 with 0 never adjacent to n.
%C A212841 Row 7 of A212835.
%H A212841 R. H. Hardin, <a href="/A212841/b212841.txt">Table of n, a(n) for n = 1..210</a>
%F A212841 Empirical: a(n) = n^8 + 8*n^7 + 14*n^6 - 16*n^5 - 30*n^4 + 24*n^3 + 8*n^2 - 8*n + 1.
%F A212841 Conjectures from _Colin Barker_, Jul 21 2018: (Start)
%F A212841 G.f.: x*(2 + 1375*x + 16177*x^2 + 23723*x^3 - 551*x^4 - 563*x^5 + 179*x^6 - 23*x^7 + x^8) / (1 - x)^9.
%F A212841 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F A212841 (End)
%e A212841 Some solutions for n=5:
%e A212841 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A212841 ..0....1....3....3....3....1....3....0....3....3....0....3....3....3....1....3
%e A212841 ..0....1....1....2....2....0....1....1....0....1....4....3....2....4....3....3
%e A212841 ..3....4....5....4....5....3....5....0....3....3....5....4....0....3....0....1
%e A212841 ..1....3....2....1....1....3....3....2....3....5....5....0....4....2....1....5
%e A212841 ..2....5....0....2....1....1....4....1....1....4....4....4....1....3....2....3
%e A212841 ..5....3....1....5....4....0....0....0....3....1....5....0....0....1....0....3
%e A212841 ..3....0....1....1....4....2....1....4....2....0....1....1....3....3....3....3
%Y A212841 Cf. A212835.
%K A212841 nonn
%O A212841 1,1
%A A212841 _R. H. Hardin_, May 28 2012