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A256815 Number of length n+7 0..1 arrays with at most two downsteps in every 7 consecutive neighbor pairs.

%I A256815 #6 Jul 23 2025 15:14:52
%S A256815 219,402,753,1424,2693,5088,9613,18104,34013,63928,120362,226816,
%T A256815 427341,804974,1516179,2855304,5376354,10123582,19065294,35907400,
%U A256815 67626166,127359488,239852341,451704432,850669960,1602023036,3017039568
%N A256815 Number of length n+7 0..1 arrays with at most two downsteps in every 7 consecutive neighbor pairs.
%C A256815 Column 7 of A256816
%H A256815 R. H. Hardin, <a href="/A256815/b256815.txt">Table of n, a(n) for n = 1..210</a>
%F A256815 Empirical: a(n) = 2*a(n-1) -a(n-2) +3*a(n-4) -2*a(n-5) +10*a(n-7) -7*a(n-8) -12*a(n-11) +9*a(n-12) -24*a(n-14) +18*a(n-15)
%e A256815 Some solutions for n=4
%e A256815 ..1....0....1....1....0....0....0....1....1....1....1....1....0....0....0....0
%e A256815 ..0....0....1....1....0....0....1....1....1....1....1....0....1....1....1....0
%e A256815 ..1....0....1....1....1....1....0....1....1....1....0....1....0....1....1....0
%e A256815 ..1....0....0....1....1....1....0....1....0....0....1....0....0....1....1....1
%e A256815 ..0....1....1....1....0....1....0....0....0....0....0....0....0....1....1....0
%e A256815 ..0....1....0....0....1....0....1....0....1....0....0....0....1....0....0....1
%e A256815 ..0....0....0....0....1....0....0....0....0....1....1....1....1....0....1....1
%e A256815 ..1....1....0....1....0....0....1....0....0....0....1....1....1....1....1....1
%e A256815 ..1....1....0....0....1....0....1....1....0....1....1....0....1....1....0....0
%e A256815 ..1....0....0....0....1....1....1....1....0....1....1....0....0....0....0....0
%e A256815 ..1....0....0....1....1....0....1....1....0....1....0....1....0....0....0....0
%Y A256815 Cf. A256816
%K A256815 nonn
%O A256815 1,1
%A A256815 _R. H. Hardin_, Apr 10 2015