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A256820 Number of length n+5 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

%I A256820 #7 Jan 21 2018 09:37:43
%S A256820 64,128,256,512,956,1656,2693,4158,6153,8792,12202,16524,21914,28544,
%T A256820 36603,46298,57855,71520,87560,106264,127944,152936,181601,214326,
%U A256820 251525,293640,341142,394532,454342,521136,595511,678098,769563,870608,981972
%N A256820 Number of length n+5 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.
%C A256820 Row 5 of A256816.
%H A256820 R. H. Hardin, <a href="/A256820/b256820.txt">Table of n, a(n) for n = 1..210</a>
%F A256820 Empirical: a(n) = (1/120)*n^5 + (1/6)*n^4 + (175/24)*n^3 - (103/6)*n^2 + (747/10)*n - 30 for n>3.
%F A256820 Empirical g.f.: x*(64 - 256*x + 448*x^2 - 384*x^3 + 124*x^4 + 16*x^5 - 7*x^6 - 8*x^7 + 4*x^8) / (1 - x)^6. - _Colin Barker_, Jan 21 2018
%e A256820 Some solutions for n=4:
%e A256820 ..0....1....0....0....0....1....0....1....0....1....1....0....1....1....0....1
%e A256820 ..0....0....0....1....0....0....0....1....1....0....1....0....0....0....0....0
%e A256820 ..0....0....0....0....1....1....0....0....1....1....1....0....1....0....1....1
%e A256820 ..1....0....0....0....0....1....1....0....0....1....0....0....1....1....1....0
%e A256820 ..1....0....1....1....0....1....1....1....0....0....1....1....1....1....1....1
%e A256820 ..0....1....0....0....0....1....1....1....0....1....0....1....0....1....0....1
%e A256820 ..1....1....1....1....0....1....0....0....0....0....1....1....1....0....1....0
%e A256820 ..1....0....0....1....0....0....0....1....0....0....0....1....0....1....0....1
%e A256820 ..1....1....0....0....0....0....1....0....0....1....1....1....1....1....1....0
%Y A256820 Cf. A256816.
%K A256820 nonn
%O A256820 1,1
%A A256820 _R. H. Hardin_, Apr 10 2015