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%I #7 Jul 20 2018 06:01:59
%S 146,461,1254,2997,6451,12766,23596,41229,68732,110111,170486,256281,
%T 375429,537592,754396,1039681,1409766,1883729,2483702,3235181,4167351,
%U 5313426,6711004,8402437,10435216,12862371,15742886,19142129,23132297
%N Number of nonnegative integer arrays of length n+5 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value n+1.
%C Row 4 of A211836.
%H R. H. Hardin, <a href="/A211838/b211838.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/48)*n^6 + (19/48)*n^5 + (51/16)*n^4 + (661/48)*n^3 + (835/24)*n^2 + (317/6)*n + 41.
%F Conjectures from _Colin Barker_, Jul 20 2018: (Start)
%F G.f.: x*(146 - 561*x + 1093*x^2 - 1210*x^3 + 781*x^4 - 275*x^5 + 41*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=3:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....0....1....1....0....1....1....1....1....1....1....0....1....1....1....1
%e ..2....1....2....2....1....2....2....1....0....2....1....1....0....2....2....2
%e ..3....0....3....0....2....1....3....2....2....1....2....2....2....1....3....3
%e ..4....2....0....3....0....0....4....3....3....2....2....3....3....0....2....4
%e ..1....3....3....4....3....3....0....1....0....1....3....2....4....3....4....3
%e ..0....3....0....4....4....4....5....4....1....3....4....3....4....4....1....5
%e ..0....4....4....5....1....3....6....2....4....4....3....4....0....4....2....0
%Y Cf. A211836.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 21 2012
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