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A256819 Number of length n+4 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

%I A256819 #7 Jan 21 2018 09:37:36
%S A256819 32,64,128,256,484,856,1424,2249,3402,4965,7032,9710,13120,17398,
%T A256819 22696,29183,37046,46491,57744,71052,86684,104932,126112,150565,
%U A256819 178658,210785,247368,288858,335736,388514,447736,513979,587854,670007,761120,861912
%N A256819 Number of length n+4 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.
%C A256819 Row 4 of A256816.
%H A256819 R. H. Hardin, <a href="/A256819/b256819.txt">Table of n, a(n) for n = 1..210</a>
%F A256819 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 A256819 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 A256819 Some solutions for n=4:
%e A256819 ..1....1....1....0....0....1....0....1....1....0....0....1....0....0....0....0
%e A256819 ..0....0....0....1....0....0....1....1....1....0....0....0....1....0....1....1
%e A256819 ..0....1....0....1....0....0....0....0....0....0....1....1....1....0....1....1
%e A256819 ..1....1....0....1....1....0....0....0....0....0....0....1....0....0....1....0
%e A256819 ..1....0....0....1....1....0....0....1....0....0....0....0....1....1....1....1
%e A256819 ..0....0....0....0....1....0....0....0....0....0....0....1....1....1....0....0
%e A256819 ..0....0....0....1....0....1....1....0....1....0....0....1....1....0....1....1
%e A256819 ..1....1....1....0....1....1....0....1....1....1....1....0....1....0....1....0
%Y A256819 Cf. A256816.
%K A256819 nonn
%O A256819 1,1
%A A256819 _R. H. Hardin_, Apr 10 2015