A256819 - OEIS

%I #7 Jan 21 2018 09:37:36

%S 32,64,128,256,484,856,1424,2249,3402,4965,7032,9710,13120,17398,

%T 22696,29183,37046,46491,57744,71052,86684,104932,126112,150565,

%U 178658,210785,247368,288858,335736,388514,447736,513979,587854,670007,761120,861912

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

%C Row 4 of A256816.

%H R. H. Hardin, <a href="/A256819/b256819.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/120)*n^5 + (1/8)*n^4 + (27/8)*n^3 - (65/8)*n^2 + (1897/60)*n + 3 for n>2.

%F Empirical g.f.: x*(32 - 128*x + 224*x^2 - 192*x^3 + 68*x^4 - 4*x^6 + x^7) / (1 - x)^6. - _Colin Barker_, Jan 21 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

%Y Cf. A256816.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2015