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A211850 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.

%I A211850 #7 Jul 20 2018 07:52:14
%S A211850 63,147,286,494,785,1173,1672,2296,3059,3975,5058,6322,7781,9449,
%T A211850 11340,13468,15847,18491,21414,24630,28153,31997,36176,40704,45595,
%U A211850 50863,56522,62586,69069,75985,83348,91172,99471,108259,117550,127358,137697,148581
%N A211850 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 A211850 Row 4 of A211849.
%H A211850 R. H. Hardin, <a href="/A211850/b211850.txt">Table of n, a(n) for n = 1..210</a>
%F A211850 Empirical: a(n) = (7/3)*n^3 + (27/2)*n^2 + (163/6)*n + 20.
%F A211850 Conjectures from _Colin Barker_, Jul 20 2018: (Start)
%F A211850 G.f.: x*(63 - 105*x + 76*x^2 - 20*x^3) / (1 - x)^4.
%F A211850 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A211850 (End)
%e A211850 Some solutions for n=3:
%e A211850 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A211850 ..1....1....0....1....1....0....0....1....1....1....1....1....1....1....1....1
%e A211850 ..1....1....0....1....1....1....1....1....1....1....1....1....1....1....0....0
%e A211850 ..1....1....1....2....2....1....1....2....1....2....0....2....2....2....0....0
%e A211850 ..2....2....1....2....2....0....2....2....2....2....0....2....2....2....0....0
%e A211850 ..2....2....2....3....2....0....2....2....2....3....2....3....3....3....2....2
%e A211850 ..2....3....2....3....3....2....3....3....3....2....0....3....3....3....2....2
%e A211850 ..3....2....2....4....2....2....2....2....3....2....0....3....1....3....3....3
%e A211850 ..2....2....3....4....2....3....2....2....4....4....3....0....1....4....3....3
%e A211850 ..2....4....3....3....4....3....2....4....4....4....3....0....1....4....3....4
%e A211850 ..4....4....4....3....2....4....4....4....2....0....4....4....4....5....4....4
%Y A211850 Cf. A211849.
%K A211850 nonn
%O A211850 1,1
%A A211850 _R. H. Hardin_, Apr 22 2012