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A211852 Number of nonnegative integer arrays of length 2n+7 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

%I A211852 #7 Jul 20 2018 08:11:50
%S A211852 588,2013,5486,12713,26163,49210,86275,142968,226230,344475,507732,
%T A211852 727787,1018325,1395072,1875937,2481154,3233424,4158057,5283114,
%U A211852 6639549,8261351,10185686,12453039,15107356,18196186,21770823,25886448,30602271
%N A211852 Number of nonnegative integer arrays of length 2n+7 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.
%C A211852 Row 6 of A211849.
%H A211852 R. H. Hardin, <a href="/A211852/b211852.txt">Table of n, a(n) for n = 1..210</a>
%F A211852 Empirical: a(n) = (71/60)*n^5 + (337/24)*n^4 + 67*n^3 + (3947/24)*n^2 + (12919/60)*n + 126.
%F A211852 Conjectures from _Colin Barker_, Jul 20 2018: (Start)
%F A211852 G.f.: x*(588 - 1515*x + 2228*x^2 - 1768*x^3 + 735*x^4 - 126*x^5) / (1 - x)^6.
%F A211852 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A211852 (End)
%e A211852 Some solutions for n=3:
%e A211852 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A211852 ..1....1....1....0....1....1....1....1....1....1....0....1....1....1....1....1
%e A211852 ..0....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
%e A211852 ..0....2....2....1....2....0....2....2....2....2....1....2....1....1....2....0
%e A211852 ..2....1....1....2....2....0....2....2....2....1....1....2....2....2....2....2
%e A211852 ..2....1....1....2....2....2....1....2....3....1....0....3....2....2....2....2
%e A211852 ..2....3....0....2....2....2....1....2....2....3....0....3....3....1....2....3
%e A211852 ..3....3....0....3....3....3....3....3....3....1....2....3....3....1....2....3
%e A211852 ..3....4....3....3....3....2....3....3....3....1....2....3....4....3....3....4
%e A211852 ..4....4....3....4....4....2....3....2....4....2....3....3....3....1....3....4
%e A211852 ..3....3....3....4....3....2....4....2....4....2....3....3....3....1....2....3
%e A211852 ..3....4....4....4....3....4....4....2....5....4....4....4....1....4....2....3
%e A211852 ..2....3....4....4....0....4....3....4....5....4....4....3....3....4....4....3
%Y A211852 Cf. A211849.
%K A211852 nonn
%O A211852 1,1
%A A211852 _R. H. Hardin_, Apr 22 2012