A212839 - OEIS

%I #12 Jul 21 2018 10:07:30

%S 2,239,2258,10727,35954,97127,226274,472943,909602,1637759,2794802,

%T 4561559,7170578,10915127,16158914,23346527,33014594,45803663,

%U 62470802,83902919,111130802,145343879,187905698,240370127,304498274,382276127

%N Number of 0..n arrays of length 6 with 0 never adjacent to n.

%C Row 5 of A212835.

%H R. H. Hardin, <a href="/A212839/b212839.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 - 12*n^3 - 3*n^2 + 6*n - 1.

%F Conjectures from _Colin Barker_, Jul 21 2018: (Start)

%F G.f.: x*(2 + 225*x + 627*x^2 - 130*x^3 - 12*x^4 + 9*x^5 - x^6) / (1 - x)^7.

%F 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>7.

%F (End)

%e Some solutions for n=5:

%e ..1....3....2....5....5....1....5....2....4....2....0....2....0....1....0....3

%e ..3....2....1....3....5....2....1....1....3....0....2....5....2....4....4....1

%e ..5....1....4....2....5....3....2....2....3....1....5....4....2....0....3....1

%e ..4....0....2....5....3....2....5....5....2....1....3....3....4....2....1....0

%e ..2....1....2....5....0....3....1....3....1....4....5....3....0....4....5....1

%e ..5....0....0....1....1....2....4....5....0....5....3....2....2....2....2....2

%Y Cf. A212835.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 28 2012