A255988 - OEIS

%I #8 Jan 24 2018 14:03:07

%S 26,45,80,144,256,451,796,1413,2510,4448,7872,13943,24718,43817,77636,

%T 137540,243712,431899,765360,1356169,2403034,4258172,7545592,13370799,

%U 23692770,41983189,74394040,131826104,233594880,413927683,733476228

%N Number of length n+4 0..1 arrays with at most one downstep in every 4 consecutive neighbor pairs.

%C Column 4 of A255992.

%H R. H. Hardin, <a href="/A255988/b255988.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +3*a(n-4) -2*a(n-5).

%F Empirical g.f.: x*(26 - 7*x + 16*x^2 + 29*x^3 - 30*x^4) / (1 - 2*x + x^2 - 3*x^4 + 2*x^5). - _Colin Barker_, Jan 24 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

%Y Cf. A255992.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 13 2015