Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Jul 20 2018 07:52:14
%S 63,147,286,494,785,1173,1672,2296,3059,3975,5058,6322,7781,9449,
%T 11340,13468,15847,18491,21414,24630,28153,31997,36176,40704,45595,
%U 50863,56522,62586,69069,75985,83348,91172,99471,108259,117550,127358,137697,148581
%N Number of nonnegative integer arrays of length 2n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.
%C Row 4 of A211849.
%H R. H. Hardin, <a href="/A211850/b211850.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (7/3)*n^3 + (27/2)*n^2 + (163/6)*n + 20.
%F Conjectures from _Colin Barker_, Jul 20 2018: (Start)
%F G.f.: x*(63 - 105*x + 76*x^2 - 20*x^3) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%e Some solutions for n=3:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....1....0....1....1....0....0....1....1....1....1....1....1....1....1....1
%e ..1....1....0....1....1....1....1....1....1....1....1....1....1....1....0....0
%e ..1....1....1....2....2....1....1....2....1....2....0....2....2....2....0....0
%e ..2....2....1....2....2....0....2....2....2....2....0....2....2....2....0....0
%e ..2....2....2....3....2....0....2....2....2....3....2....3....3....3....2....2
%e ..2....3....2....3....3....2....3....3....3....2....0....3....3....3....2....2
%e ..3....2....2....4....2....2....2....2....3....2....0....3....1....3....3....3
%e ..2....2....3....4....2....3....2....2....4....4....3....0....1....4....3....3
%e ..2....4....3....3....4....3....2....4....4....4....3....0....1....4....3....4
%e ..4....4....4....3....2....4....4....4....2....0....4....4....4....5....4....4
%Y Cf. A211849.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 22 2012