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Number of length n+6 0..1 arrays with at most two downsteps in every 6 consecutive neighbor pairs.
1

%I #7 Jan 24 2018 09:30:02

%S 120,229,442,856,1656,3204,6192,11955,23088,44617,86226,166620,321960,

%T 622104,1202016,2322567,4487848,8671757,16756074,32377024,62560664,

%U 120883084,233577104,451331323,872088416,1685098737,3256043394

%N Number of length n+6 0..1 arrays with at most two downsteps in every 6 consecutive neighbor pairs.

%C Column 6 of A256816.

%H R. H. Hardin, <a href="/A256814/b256814.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -a(n-4) +3*a(n-6) -2*a(n-7) -6*a(n-9) +4*a(n-10).

%F Empirical g.f.: x*(120 - 11*x + 104*x^2 - 39*x^3 + 48*x^4 + 93*x^5 - 190*x^6 - 128*x^7 - 250*x^8 + 252*x^9) / ((1 - x)*(1 - x - 2*x^3 - x^4 - x^5 - 4*x^6 - 2*x^7 - 2*x^8 + 4*x^9)). - _Colin Barker_, Jan 24 2018

%e Some solutions for n=4:

%e ..1....1....0....0....1....1....1....0....1....0....1....1....0....0....0....0

%e ..1....0....1....0....0....1....0....1....0....0....0....0....0....1....0....0

%e ..1....0....0....1....0....1....0....1....1....0....0....0....0....0....1....1

%e ..0....0....1....1....1....1....0....0....1....1....0....1....1....0....1....0

%e ..1....0....1....1....0....0....0....0....0....0....1....0....1....0....0....1

%e ..1....1....1....1....1....1....0....0....1....0....0....0....0....0....1....0

%e ..1....0....1....0....1....1....0....1....1....0....0....1....0....1....0....0

%e ..1....1....0....1....0....1....0....0....1....1....1....1....1....0....0....0

%e ..0....0....0....0....0....0....0....1....0....0....0....1....1....0....1....1

%e ..1....0....1....1....0....0....0....0....1....0....0....1....1....1....1....0

%Y Cf. A256816.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2015