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A211851 Number of nonnegative integer arrays of length 2n+6 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.

%I A211851 #7 Jul 20 2018 08:01:58
%S A211851 196,561,1302,2619,4755,7996,12671,19152,27854,39235,53796,72081,
%T A211851 94677,122214,155365,194846,241416,295877,359074,431895,515271,610176,
%U A211851 717627,838684,974450,1126071,1294736,1481677,1688169,1915530,2165121,2438346
%N A211851 Number of nonnegative integer arrays of length 2n+6 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.
%C A211851 Row 5 of A211849.
%H A211851 R. H. Hardin, <a href="/A211851/b211851.txt">Table of n, a(n) for n = 1..210</a>
%F A211851 Empirical: a(n) = (43/24)*n^4 + (185/12)*n^3 + (1217/24)*n^2 + (937/12)*n + 50.
%F A211851 Conjectures from _Colin Barker_, Jul 20 2018: (Start)
%F A211851 G.f.: x*(196 - 419*x + 457*x^2 - 241*x^3 + 50*x^4) / (1 - x)^5.
%F A211851 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 A211851 (End)
%e A211851 Some solutions for n=3:
%e A211851 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A211851 ..0....1....1....1....0....1....0....1....1....1....1....1....1....0....1....1
%e A211851 ..1....1....1....1....1....0....1....0....1....1....1....1....1....0....1....1
%e A211851 ..1....1....2....1....1....0....1....0....2....2....2....2....2....1....2....1
%e A211851 ..2....2....2....2....2....2....1....2....2....2....1....2....1....1....2....2
%e A211851 ..2....1....2....1....1....2....2....2....2....3....1....2....1....2....3....1
%e A211851 ..3....1....3....1....1....3....2....2....3....2....1....3....3....2....2....1
%e A211851 ..3....3....3....1....1....3....0....3....3....2....1....3....3....3....2....3
%e A211851 ..0....3....3....3....3....3....0....3....3....4....3....4....4....3....3....3
%e A211851 ..0....4....4....3....3....3....3....2....4....2....3....3....3....4....2....4
%e A211851 ..4....4....3....4....4....4....3....2....4....4....3....3....4....3....2....4
%e A211851 ..0....5....3....3....3....4....4....4....3....2....4....0....4....4....4....2
%Y A211851 Cf. A211849.
%K A211851 nonn
%O A211851 1,1
%A A211851 _R. H. Hardin_, Apr 22 2012