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Number of 0..7 arrays x(0..n+1) of n+2 elements without any two consecutive increases.
1

%I #13 Oct 15 2017 20:26:29

%S 456,3270,23136,164004,1160616,8216484,58154912,411637168,2913595712,

%T 20622837480,145970677056,1033197881712,7313093248992,51762926098992,

%U 366383987227392,2593308396911680,18355737644921600,129924040926296800

%N Number of 0..7 arrays x(0..n+1) of n+2 elements without any two consecutive increases.

%C Column 7 of A200785.

%H R. H. Hardin, <a href="/A200784/b200784.txt">Table of n, a(n) for n = 1..210</a>

%H A. Burstein and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0112281">Words restricted by 3-letter generalized multipermutation patterns</a>, Annals. Combin., 7 (2003), 1-14. See Th. 3.13.

%F Empirical: a(n) = 8*a(n-1) -56*a(n-3) +70*a(n-4) -28*a(n-6) +8*a(n-7).

%F Empirical g.f.: 2*x*(228 - 189*x - 1512*x^2 + 2226*x^3 - 108*x^4 - 864*x^5 + 256*x^6) / ((1 - 2*x)*(1 + 2*x - 2*x^2)*(1 - 8*x + 6*x^2 + 4*x^3 - 2*x^4)). - _Colin Barker_, Oct 15 2017

%e Some solutions for n=3

%e ..7....5....7....4....5....2....3....7....5....5....5....6....1....5....4....4

%e ..0....5....4....2....3....2....1....4....0....5....7....4....0....5....4....4

%e ..0....5....4....1....6....6....3....5....0....4....6....6....6....7....4....4

%e ..0....1....7....1....5....5....0....0....6....1....6....3....0....0....4....7

%e ..1....4....0....6....5....2....6....5....3....4....2....4....1....2....4....3

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2011