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A255991 Number of length n+7 0..1 arrays with at most one downstep in every 7 consecutive neighbor pairs.

%I A255991 #8 Jan 25 2018 11:57:19
%S A255991 93,136,207,328,530,854,1352,2088,3175,4824,7406,11528,18124,28562,
%T A255991 44768,69584,107469,165670,256009,397452,619647,967640,1509297,
%U A255991 2347848,3643074,5646004,8753601,13591820,21137644,32901050,51205059,79628272,123712139
%N A255991 Number of length n+7 0..1 arrays with at most one downstep in every 7 consecutive neighbor pairs.
%C A255991 Column 7 of A255992.
%H A255991 R. H. Hardin, <a href="/A255991/b255991.txt">Table of n, a(n) for n = 1..210</a>
%F A255991 Empirical: a(n) = 2*a(n-1) -a(n-2) +6*a(n-7) -5*a(n-8).
%F A255991 Empirical g.f.: x*(93 - 50*x + 28*x^2 + 50*x^3 + 81*x^4 + 122*x^5 + 174*x^6 - 320*x^7) / (1 - 2*x + x^2 - 6*x^7 + 5*x^8). - _Colin Barker_, Jan 25 2018
%e A255991 Some solutions for n=4:
%e A255991 ..0....1....1....0....0....0....1....1....0....1....1....0....0....0....0....0
%e A255991 ..0....0....1....0....0....1....1....1....1....0....1....1....0....1....1....0
%e A255991 ..1....0....0....1....1....0....1....1....0....0....1....1....0....1....1....0
%e A255991 ..0....0....0....0....0....0....0....1....0....0....1....1....0....0....1....0
%e A255991 ..1....0....1....1....0....0....0....1....1....0....1....1....0....0....1....0
%e A255991 ..1....1....1....1....1....1....0....1....1....1....0....1....0....0....1....1
%e A255991 ..1....1....1....1....1....1....0....1....1....1....0....1....1....0....1....0
%e A255991 ..1....1....1....1....1....1....0....0....1....1....0....1....1....1....1....0
%e A255991 ..1....1....1....1....1....1....1....1....1....0....1....0....1....1....0....0
%e A255991 ..1....1....0....1....1....0....1....1....1....0....1....0....1....1....1....0
%e A255991 ..0....0....0....1....0....1....0....1....1....0....1....0....0....0....1....1
%Y A255991 Cf. A255992.
%K A255991 nonn
%O A255991 1,1
%A A255991 _R. H. Hardin_, Mar 13 2015