|
%I #10 Jul 21 2018 10:07:16
%S 2,41,178,497,1106,2137,3746,6113,9442,13961,19922,27601,37298,49337,
%T 64066,81857,103106,128233,157682,191921,231442,276761,328418,386977,
%U 453026,527177,610066,702353,804722,917881,1042562,1179521,1329538
%N Number of 0..n arrays of length 4 with 0 never adjacent to n.
%C Row 3 of A212835.
%H R. H. Hardin, <a href="/A212837/b212837.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^4 + 4*n^3 - 4*n + 1.
%F Conjectures from _Colin Barker_, Jul 21 2018: (Start)
%F G.f.: x*(2 + 31*x - 7*x^2 - 3*x^3 + x^4) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=5:
%e ..2....5....3....5....0....0....4....3....2....0....3....4....2....4....5....4
%e ..5....5....3....1....0....0....1....5....4....2....0....2....1....2....2....4
%e ..1....5....1....0....1....2....1....5....3....4....0....2....1....1....3....1
%e ..2....3....3....4....1....5....4....4....5....4....3....5....4....1....1....2
%Y Cf. A212835.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 28 2012
|
